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2003 Fiscal Year Final Research Report Summary

Qualitative Theory on Oscillation of Solutions of Differential Equations

Research Project

Project/Area Number 14540162
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionToyama University

Principal Investigator

YOSHIDA Norio  Toyama University, Facuty of Science, Professor, 理学部, 教授 (80033934)

Co-Investigator(Kenkyū-buntansha) FUJITA Yasuhiro  Toyama University, Facuty of Science, Assistant Professor, 理学部, 助教授 (10209067)
IKEDA Hideo  Toyama University, Facuty of Science, Professor, 理学部, 教授 (60115128)
Project Period (FY) 2002 – 2003
Keywordsdifferential equations / qualitative theory / partial factional-differential equations / oscillation / zero
Research Abstract

Various extended results were obtained for qualitative theory on oscillation of solutions of partial functional-differential equations, that is, oscillation theory. Sufficient conditions for every solution of parabolic equations of neutral type to be oscillatory were established. Moreover, oscillation theorems for a generalization of the classical Rosenau-Burgers equation were obtained^Oscillation theory for vector parabolic and hyperbolic equations could be constructed. Neutral hyperbolic equations of discrete type have been treated, but we could make oscillation theory for hyperbolic equations with continuous distributed deviating arguments. Three papers on this subject were submitted for publication. Two of them are joint works with Professor Youshan Tao of Dong Hua University in P.R.China. A paper on tumor which is a joint work was accpted for publication in the journal "Ndnlinearity". Furthermore, a joint paper with Professor Litan Yan of Dong Hua University which treat oscillation theory of characteristic initial value problems for hyperbolic equations of hyperbolic type was submitted for publication. I have given an invited lecture at the international conference(Conference on Differential Equations and Applications) held in Slovakia. Then I could discuss with Slovakian Mathematicians, and I could cooperate with Professor Jaros(Comenius University) to establish Picone identities and make Sturmian comparison theorems for half-linear elliptic equations with first order terms. I could hold "Toyama Conference on Differential Equations-2003" at Toyama University, and have fruitful discussions about Mathematics with the guest speaker, Professor E. Minchev of Chiba University.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] Y.Tao: "Nonlinear analysis of a model of vascular tumor growth and treatment"Nonlinearity. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Shoukaku: "Oscillatory properties of solutions of nonlinear parabolic equations with functional arguments"Indian Journal of Pure and Applied Mathematics. 34. 1469-1478 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Minchev: "Oscillations of venctor differential equations of hyperbolic type with functional arguments"Mathmatics Houranl of Toyama University. 26. 75-84 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Minchev: "Forced oscillations of solutions of a class of higher order nonlinear parabolic equations"Advanced Studies in Contemporary Mathematics. 6. 165-171 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Shoukaku: "Oscillation criteria for a class of parabolic equations with functional arguments"Kyungpook Mathematical Journal. 43. 263-272 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Minchev: "Oscillation of solutions of vector differential equatinos of parabolic type with functional arguments"Journal of Computational and Applied Mathematics. 151. 107-117 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Tao, N.Yoshida, Q.Guo: "Nonlinear analysis of a model of vascular tumor growth and treatment"Nonlinearity. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Shoukaku, N.Yoshida: "Oscillatory properties of solutions of nonlinear parabolic equations with functional arguments"Indian J.Pure Appl.Math.. Vol.34. 1469-1478 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Minchev, N.Yoshiday: "Oscillations of vector differential equations of hyperbolic type with functional arguments"Math.J.Toyama Univ.. Vol.26. 75-84 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Minchev, N.Yoshiday: "Forced oscillations of solutions of a class of higher order nonlinear parabolic equations"Adv.Stud.Contemp.Math.. Vol.6. 165-171 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Shoukaku, N.Yoshida: "Oscillation criteria for a class of parabolic equations with functional arguments"Kyungpook Math.j.. Vol.43. 263-272 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Minchev, N.Yoshiday: "Oscillations of solutions of vector differential equations of parabolic type with functional arguments"J.Comput.Appl.Math.. Vol.151. 107-117 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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