関数方程式に付随する複雑集合の総合解析

2000 Fiscal Year Annual Research Report

• Project/Area Number: 12440040
• Research Institution: Shimane University
• Principal Investigator: 相川 弘明 島根大学, 総合理工学部, 教授 (20137889)
• Co-Investigator(Kenkyū-buntansha): 水田 義弘 広島大学, 総合科学部, 教授 (00093815) ; 杉江 実郎 島根大学, 総合理工学部, 教授 (40196720) ; 山崎 稀嗣 島根大学, 総合理工学部, 教授 (70032935) ; 原 惟行 大阪府立大学, 工学部, 教授 (20029565) ; 村田 實 東京工業大学, 理学部, 教授 (50087079)
• Keywords: ポテンシャル / 調和 / ソボレフ関数 / 境界条件 / 放物型 / 安定性 / 関数微分方程式 / ボルテラ型微分方程式

Research Abstract

・ 一様John領域のMartin境界の決定を行い、3次元Sierpinski Gasketに応用した.Mittag-Leffler研究所・研究報告集に掲載.またHolder連続な境界関数に対するDirichlet問題がHolder連続な解を持つための条件を求めた.(相川)
・ 中立型積分方程式の解・周期解・概周期解の存在、不動点定理の常微分・関数微分方程式の解の安定性理論への応用、及び関数微分方程式の解の有界性と概周期性の関連.(古用)
・ ボルテラ型微分方程式に対応する力学系の構成をし,安定性および非線形振動論へ応用した.また概周期解の存在に関する解析的および力学系から考察した.(日野)
・ Orlicz族の関数のRiesポテンシャルの研究の微分可能性とHolder連続性,および重みつきソボレフ関数の境界挙動.(水田,下村,二村)
・ Liouvilleの定理とBocherの定理の多調和関数への一般化.(水田,岸,二村)
・ タイムラグをもつ2次元線形微分方程式が漸近周期解持つための必要十分条件を求め、応用として非線形項を持つ場合のホップ分岐を調べた.(原)
・ 多様体や領域上の放物型方程式に対するCauchy問題の正の解の一意性を示した.(村田)

Research Products

• [Publications] H.Aikawa: "Martin boundary of a fractal domain"Institut Mittag-Leffler, Report. 40. (2000)
• [Publications] H.Aikawa,S.Gardinder: "Evaluation of superharmonic functions using limits along lines"Bull.London Math.Soc.. 32. 209-213 (2000)
• [Publications] H.Aikawa: "Boundary Harnack principle and Martin boundary for a uniform domain"J.Math.Soc.Japan. 53. 119-145 (2001)
• [Publications] T.A.Burton and T.Furumochi: "Periodic and asymptotically periodic solutions of neutral integral equations"E.J.Qualitative Theory of Differential Equations. 10. 1-27 (2000)
• [Publications] T.A.Burton and T.Furumochi: "Existence theorems and periodic solutions of neutral integral equations"Nonlinear Analysis. (to appear).
• [Publications] T.A.Burton and T.Furumochi: "Fixed points and problems in stability theory for ordinary and functional differen tial equations"Dynamic Systems and Applications. (to appear).
• [Publications] T.A.Burton and T.Furumochi: "Krasnoselskii's fixed point theorem and stability"Nonlinear Analysis. (to appear).
• [Publications] T.Furumochi,T.Naito,N.V.Minh: "Boundedness and almost periodicity of solutions of partial functional differential equations"J.Differential Equations. (to appear).
• [Publications] Y.Mizuta and T.Shimomura: "Growth properties of spherical means for monotone BLD functions in the unit ball"Acad.Sci.Fenn.Ser.A.I.Math.. 25. 457-465 (2000)
• [Publications] Y.Mizuta and T.Shimomura: "Differentiability and Holder continuity of Riesz potentials of functions in Orlicz classes"Analysis. 20. 201-223 (2000)
• [Publications] Y.Mizuta: "Boundary limits of functions in weighted Lebesgue or Sobolev classes"Revue Roumaine Math.Pures Appl.. 45(to appear). (2000)
• [Publications] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of the Liouville theorem to polyharmonic functions"J.Math.Soc.Japan. 53. 113-118 (2001)
• [Publications] T.Futamura,K.Kishi,Y.Mizuta: "A generalization of Bocher's theorem for polyharmonic functions"Hiroshima Math.J.. 31(to appear). (2001)
• [Publications] T.Futamura and Y.Mizuta: "Existence of functions in weighted Sobolev spaces"Nagoya Math.J.. 31(to appear). (2001)
• [Publications] Oettli,W.,山崎稀嗣: "Duality theorems on an infinite network"Optimization. 48. 1-15 (2000)
• [Publications] 村上温,山崎稀嗣: "Inequalities on infinite networks"Mem.Fac.Sci.Shimane Univ.Ser.B : Mathematical Science. 33(to appear). 47-62 (2000)
• [Publications] 陳小君,生源寺亨浩,山崎稀嗣: "Verification for existence of solutions of linear complementarity problems"Linear Algebra and Its Applications. (to appear). (2000)
• [Publications] 谷口雅彦: "整函数の構成:断章"数理解析研究所講究録. 1153. 103-112 (2000)
• [Publications] E.Fujikawa,H.Shiga and M.Taniguchi: "Discreteness of the mapping class group for Riemann surfaces of infinite ana lytic type"Proc.of the 2-nd ISAAC Congress. 2000. 1015-1023
• [Publications] K.Ishige and M.Murata: "Uniqueness of nonnegative solutions of the cauchy problem for parabolic equations on manifolds or domains"Ann.Scuola Normale Sup.Pisa. (to appear).
• [Publications] Y.Hino,S.Murakami: "Almost periodic quasi-processes and the existence of almost periodic solutions"Proceedings of international conference of biomathematics, bioinformatics and applications of functional differential equations, Akdeniz University. 94-103 (2000)
• [Publications] Y.Hino,T.Naito,N.V.Minh,J.S.Shin: "Almost Periodic Solutions of Differential Equations in Banach Space"Gordon and Breach. (to appear). (2000)
• [Publications] Y.Hino,S.Murakami: "Quasi-processes and stabilities in functional differential equations"Nonlinear Analysis. (to appear).
• [Publications] Y.Hino,S.Murakami: "Total Stability in abstract functional differential equations with infinite delay"Electronic J.of Qualitative Theory of Differential Equations. 13. 1-9 (2000)
• [Publications] Y.Hino,S.Murakami,T.Naito,N.V.Minh: "A variation-of-constants formula for abstract functional differential equations in the phase space"J.of Differential Equas. (to appear).
• [Publications] Y.Hino,S.Murakami: "Limiting equations and some stability properties for asymptotically almost periodic functional differential equations with infinite delay"Tohoku Math.J.. (to appear).
• [Publications] T.Hara,R.Miyazaki,T.Morii: "Asymptotic periodic solutions for linear differential-difference equations with N delays and Hopf bifurcation"Funkcialaj Ekvacioj. 43. 193-212 (2000)
• [Publications] W.Ma,T.Hara,Y.Takeuchi: "Stability of a 2-dimensional neural network with time delays"Journa1 of Biological Systems. 8. 177-193 (2000)
• [Publications] R.Ogita,H.Matsunaga,T.Hara: "Asymptotic stability condition for a class of linear delay difference equations of higher order"J.Math.Anal.Appl.. 248. 83-96 (2000)
• [Publications] S.Sakata and T.Hara: "Dynamics of a linear differential system with piecewise constant argument"Dynam.Contin.Discrete Impuls.Systems. 7. 585-594 (2000)