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Poincare-Bendixson type theoreom for holomorphic foliation of codimension one and its application

Research Project

Project/Area Number 13640092
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionRyukoku University

Principal Investigator

ITO Toshikazu  Ryukoku Univ., Faculty of Economics, Professor, 経済学部, 教授 (60110178)

Co-Investigator(Kenkyū-buntansha) KOKUBO Hiroe (OKA Hiroe)  Ryukoku Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (20215221)
YOTSUTANI Shoji  Ryukoku Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (60128361)
MATSUMOTO Waichiro  Ryukoku Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (40093314)
YAMAGISHI Yoshikazu  Ryukoku Univ., Faculty of Sci.and Tech., Assistant, 理工学部, 助手 (40247820)
MORITA Yoshihisa  Ryukoku Univ., Faculty of Sci.and Tech., Professor, 理工学部, 教授 (10192783)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsholomorphic one form / holomorphic foliation / Poincare-Bendixson theorem / Poincare-Hopf theorem / holomorphic vector field / singularity / transversality / 正則1型式 / Kacの問題 / 半線形楕円型方程式 / ホモクリニック軌道 / 分岐 / ニュートン法 / カントール族 / 正則1-形式 / Oseenの螺旋流 / ギンツブルグ・ランダウ方程式 / 渦糸解 / 複素葉層構造 / 複素力学系 / 共形スカラー曲率方程式 / ホモクリニック分岐 / 特異極限 / 周期的不定点 / 南雲型Cauchy-Kowalevskaya定理
Research Abstract

The aim of this project is an extension of "Poincare-Bendixson type theorem for holomorphic vector field" proved by A.Douady and T.Ito to a holomorphic foliation of codimension one. We will investigate the following question :
Question Let F be a holomorphic foliatiop of codimension one defined in a neighborhood of a closed disc <B^<2n>(R)>^^^-={Z∈C^n||Z|【less than or equal】R}⊂C^n. If F is transverse to S^<2n-1>(R)=∂<B^<2n>(R)>^^^-, then what can be said about F?
We got the following results :
(1)There is no holomorphic foliation F such that F is transverse to S^<4m+1>(R)⊂C^<2m+1>.
(2)If F is defined by a homogeneous integrable one form ω, F is not transverse to S^<2n-1>(R), n【greater than or equal】3.
(3)Let F be defined in a neighborhood U of a closed polydisk <Δ^n(1)>^^^-⊂C^n. If F is transverse a boundary of <Δ^n(1)>^^^-, then F is ψ^*(L), where L is a hyperbolic linear logarithmic foliation on C^n and a map ψ:U→C^n is holomorphic.
(4)Let ω be a holomorphic one form defined in a neighborhood of <B^<2n>(R)>^^^-⊂C^n. If Ker(ω) is transverse to S^<2n-1>(R), then we have a Poincare-Hopf type theorem for ω.
(5)If Ker(ω) is transverse to S^<2n-1>(R), then there is only one singular point of ω inside B^<2n>(R) and this point is simple.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (82 results)

All Other

All Publications (82 results)

  • [Publications] T.Ito: "An application of the Cayley number to a holomorphic foliation on C^4"龍谷紀要. 24-1. 17-22 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "On holomorphic one-forms transverse to closed hypersurfaces"Annals. of Brazilian Academy of Sciences. 75-3. 265-269 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "Holomorphic foliations of codimension one transverse to polydiscs"J.fur die reine und angew.Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "A Poincare-Hopf type theorem for holomorphic one-forms"Topology. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differential operators and related problems. 145-156 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] W.Matsumoto, M.Murai, S.Yotsutani: "By which kind of sound, can one hear the shape of drum?"数理解析研究所講究録「波動現象と漸近解析」. 1315. 156-175 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc.Roy.Soc.Edinburgh Sect.A. 131. 647-665 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J.Indust.Appl.Math.. 18. 503-519 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its applications"Taiwanese J.Math.. 5. 507-517 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for scalar curvature equation"Differential Integral Equations. 14. 273-288 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Comm.Pure Appl.Anal.. 1. 85-102 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Myogahara, E.Yanagida, S.Yotsutani: "Structure of positive radial solutions for semilinear Dirichlet Problems on a ball"Funkcial.Ekvac.. 45. 1-21 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows"Communication of Pure and Applied Analysis. 3-3. 381-390 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equqtions : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl.. 2-211. 121-137 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Lou, W.-M.Ni, S.Yotsutani: "On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion"Discrete and Continuous Dynamical Systems. 10-1. 435-458 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Oka: "Conley index theory for slow-fast systems : multi-dimensional slow manifold"Proceedings of Equadiff 2003. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita, J.Dockery, M.Pernarowski: "Symmetry Breaking Homoclinic Bifurcations in Diffusively Coupled Equations"J.Dynamics and Differential Equations. 13. 613-649 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Notes on the Limit Equation of Vortex Motion for the Ginzburg-Landau Equation with Neumann Condition"Japan J.Indust.Appl.Math.. 18. 483-501 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Vortex Dynamics for the Ginzburg-Landau Equation with Neumann Condition"Methods Appl.Anal.. 8. 451-478 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita: "Some Dynamical Aspects of Vortices in the Ginzburg-Landau Equation"数理解析研究所講究録. 1249. 47-51 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Ginzburg-Landau Equation with Magnetic Effect in a Thin Domain"Calc.Var.Partial Differential Equations. 15. 325-352 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukano, Y.Morita, H.Ninomiya: "Some entire solutions of the Allen-Cahn equation"Taiwanese J.Math.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita: "Stable Solutions to the Ginzburg-Landau Equation with Magnetic Effect in a Thin Domain"Japan J.Indust.Appl.Math.. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.-S.Guo, Y.Morita: "Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations"Discrete and Continuous Dynamical Systems. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Yamagishi: "Quadratically convergent initial values to a double root in Newton's method of two variables"Progress in Analysis, Proceedings of the 3rd ISAAC Congress. 563-569 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Yamagishi: "On the local convergence of Newton's method to a multiple root"Journal of the Mathematical Society of Japan. 55-4. 897-908 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito: "An application of the Cayley number to a holomorphic foliation on C^4"Ryukoku Kiyou. 24-1. 17-22 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "On holomorpahic one-forms transverse to closed hypersurfaces"Annals.of Brazilian Academy of Sciences. 75-3. 265-269 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "Holomorphic foliations of codimension one transverse to polydiscs"J.fur die reine und angew.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "A Poincare-Hopf type theorem for holomorphic one-forms"Topology. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differetitial operators and related problems. 145-156 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] W.Matsumoto, M.Murai, S.Yotsutani: "By which kind of sound, can one hear the shape of drum?"RIMS. 1315. 156-175 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc.Roy.Soc.Edinburgh Sect.A. 131. 647-665 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J.Indust.Appl.Math.. 18. 503-519 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its applications"Taiwanese J.Math.. 5. 507-517 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for scalar curvature equation"Differential Integral Equations. 14. 273-288 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Kabeya, B.Yanagida, S.Yotsutani: "Canonical foarms and structure theorems for radial solutions to semi-linear elliptic problems"Comm.Pure Appl.Anal.. 1. 85-102 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Myogahara, B.Yanagida, S.Yotsutani: "Structure of positive radial solutions for semilinear Dirichlet Problems"Funkcial.Ekvac.. 45. 1-21 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows"Communication on Pure and Applied Analysis. 3-3. 381-390 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl.. Series2-211. 121-137 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Lou, W.-M.Ni, S.Yotsutani: "On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion"Discrete and Continuous Dynamical Systems. 10-1. 435-458 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Oka: "Conley index theory for slow-fast systems : multi-dimensional slow manifold"Proceedings of Equadiff 2003. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita, J.Dockery, M.Pernarowski: "Symmetry Breaking Homoclinic Bifurcations in Diffusively Coupled Equations"J.Dynamics and Differential Equations. 13. 613-649 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Notes on the Limit Equation of Vortex Motion for the Ginzburg-Landau Equation with Neumann Condition"Japan J.Indust.Appl.Math.. 18. 483-501 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Vortex Dynamics for Ginzburg-Landau Equation with Neumann Condition"Methods Appl.Anal.. 8. 451-478 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita: "Some Dynamical Aspects of Vortices in the Ginzburg-Landau Equation"RIMS. 1249. 47-51 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Jimbo, Y.Morita: "Ginzburg-Landau Equation with Magnetic Effect in a Thin Domain"Calc.Var.Partial Differential Equations. 15. 325-352 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Fukano, Y.Morita, H.Ninomiya: "Some entire solutions of the Allen-Cahn equation"Taiwanese J.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Morita: "Stable Solutions to the Ginzburg-Landau Equation with Magnetic Effect in a Thin Domain"Japan J.Indust.Appl.Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] J.-S.Guo, Y.Morita: "Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations"Discrete and Continuous Dynamical Systems. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Yamagishi: "Quadratically convergent initial values to a double root in Newton's method of two variables"Progress in Analysis, Proceedings of the 3rd ISAAC Congress(2003). 563-569 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Yamagishi: "On the local convergence of Newton's method to a multiple root"Journal of the Mathematical Society of Japan. 55-4. 897-908 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ito, B.Scardua: "On holomorphic one-forms transverse to closed hypersurfaces"Annals of Brazilian Academy of Sciences. 75-3. 265-269 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ito, B.Scardua: "Holomorphic foliations of codimension one transverse to polydiscs"J.fur die reine undangew.Math.. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ito, B.Scardua: "A Poincare-Hopf type theorem for holomorphic one-forms"Topology. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differential operators and related problems, ed.V.Ancina et al.. 145-156 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] W.Matsumoto, M.Murai, S.Yotsutani: "By which kind of sound, can one hear the shape of drum?"数理解析研究所講究録「波動現象と漸近解析」. 1315. 156-175 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary-value problem arising in Ossen's spiral flows"Communication on Pure and Applied Analysis. 3-3. 381-390 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl., Series. 2-211. 121-137 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Lou, W.M.Ni, S.Yotsutani: "On a Limiting System in the Lotka - Volterra Competition with Cross-Diffusion"Discrete and Continuous Dynamical Systems. 10-1. 435-458 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Fukao, Y.Morita, H.Ninomiya: "Some entire solutions of the Allen-Cahn equation"Taiwanese J.Math.. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Morita: "Stable Solutions to the Ginzburg-Londau Equation with Magnetic Effect in a Thin Domain"Japan J.Indust.Appl.Math.. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] J.S.Guo, Y.Morita: "Entire solutions of rection-diffusion equations and an application to discrete diffusive equations"Discrete and Contin.Dynam.Systems. (to appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yamagishi: "Quadratically convergent initial values to a double root in Newton's method of two variables"Progress in Analysis, proceedings of the 3rd ISAAC Congress (2003), World Scientific. 563-569 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Yamagishi: "On the local convergence of Newton's method to a multiple root"J.of the Math.Society of Japan. 55-4. 897-908 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Ito: "An application of the Cayley number to a holomorphic foliation on C^4"The Ryukoku Journal of Humanities and Sciences. 24-1. 17-22 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary value problem arising in Oseen's spiral flows"Communication on Pure and Applied Analysis. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Lou, W.W.Ni, Wei-Mlng, S.Yotsutani: "On a limiting system in the Lotka-Volterra Competition with cross-diffusion"Discrete and Continuous Dynamical Systems. (to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Myogahara, E.Yanagida, S.Yotsutani: "Structure of positive radial solutions for semi-linear Dirichlet problems on a ball"Funkcial.Ekvac.. 45-1. 1-21 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communication on Pure and Applied Analysis. 1-1. 85-102 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Jimbo, Y.Morita: "Ginzburg-Landau equation with magnetic effect in a thin domain"Calc.Var.Partial Differential Equations. 15. 325-352 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Yamagishi: "Cantor bouquet of holomorphic stable manifolds for a periodec indeterminate point"Nonlinearity. 14. 113-120 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Ito: "Some examples and problems of contact sets (polar varieties) of spheres and holomorphic vector fields"The Ryukoku Journal of Humanities and Sciences. 22-2. 145-152 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14-3. 273-288 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] E.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J. Indust. Appl. Math.. 18-2. 503-519 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc. Roy. Soc. Edinburgh Sect. A. 131-3. 647-665 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its apllications"Taiwanese J. Math.. 5-3. 507-517 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communication on Pure and Applied Analysis. 1(to appear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Lou, W.M.Ni, S.Yotsutani: "On a limiting system in the Lotka-Volterra competition with cross-diffusion"Discrete and Continuous Dynamical Systems. (to appear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differential operators and related problems, ed. V. Ancina et al., Marcel Dekker. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Morita, J.Dookery, M.Pernarowski: "Symmetry Breaking homoclinic bifurcations in difurcations in diffusively coupled equations"J. Dynamics and Differential Equations. 13. 613-649 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Jimbo, Y.Morita: "Notes on the limit equation of Vortex Motion for the Ginzburg-Landou equation with Neumann condition"Japan J. Indust, Appl. Math.. 18. 483-501 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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