Project/Area Number  10640208 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Global analysis

Research Institution  Hiroshima University 
Principal Investigator 
柴田 徹太郎 広島大, 総合科学部, 助教授 (90216010)
USAMI Hiroyuki Hiroshima University, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (90192509)

CoInvestigator(Kenkyūbuntansha) 
TANAKA Kazunaga Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (20188288)
YOSHIDA Kiyoshi Hiroshima University, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (80033893)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  eigenvalue problem / elliptic equation / positive solution / 固有値問題 / 楕円型方程式 / 正値解 / 準線形常微分方程式 / 非線形 / 楕円形方程式 / 固有値 
Research Abstract 
(1) Eigenvalue Problems of Elliptic Equations : Twoparameter eigenvalue problems for semilinear elliptic equations are studied. We establish asymptotic properties of (variational) eigenvalues and eigenfunctions. Twoparameter AmbrosettiProdi problems are also studied. We investigate the relation between parameters and the number of solutions. (2) Positive Solutions of Elliptic Equations : Semilinear secondorder elliptic euations are considered in unbounded domains. We establish multiplicity results for positive solutions and uniqueness theorems for positive solutions. (3) Positive Solutions of Quasilinear Ordinary Differential Equations : Quasilinear ordinary differential equations whose leading term is onedimensionai pseudoLaplacian are considered. We obtain asynrptotic representations of positive solutions. As an application of these results, we show existence of several types of positive solutions of exterior Dirichlet problems for quasilinear elliptic equations. (4) Mathematical Models Describing Aggregation Phenomena of Molds : We consider selfsimilar solutions of parabolic systems introduced by Keller and Segel to describe aggregation phenomena of molds due to chemotaxis. We clarify the relation between parameters and the number of selfsimilar solutions. (5) Nonnegative Nontrivial Solutions of Quasilinear Elliptic Equations and Elliptic Systems : We establish necessary and/or sufficient conditions for quasilinear elliptic equations, as well as quasilinear elliptic systems, to possess nontrivial nonnegative entire solutions. Several Liouville type theorems are also obtained.
