带小参数的半线性椭圆方程Dirichlet边值问题的可解性  

Solvability of Dirichlet Boundary Value Problems for Semilinear Elliptic Equations with Small Parameters

作　　者：石曼 钟金标 SHI Man;ZHONG Jinbiao(School of Mathmatics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2020年第2期29-31,共3页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金研究项目(1608085MA/4)。

摘　　要：本文讨论了一类带小参数的半线性椭圆方程Dirichlet边值问题的可解性。利用非线性项满足的条件,将非线性项划为线性部分与次线性部分,并利用不动点定理、算子理论、调和函数极限原理、Green第一恒等式和Poincare不等式等理论和方法,讨论了此类带小参数的半线性椭圆型方程边值问题正解的存在性和正解的唯一性及正解的不存在性,证明了相应的定理,同时作为定理的应用给出了实例。This paper discusses the solvability of a class of semi-linear elliptic equation Dirichlet boundary value problems with small parameters.The nonlinear term is divided into linear part and sublinear part by the condition that the nonlinear term satisfies.The theory and method of fixed-point theorem,operator theory,harmonic function limit principle,Green first identity and Poincare inequality are discussed.The existence of positive solutions and the uniqueness of positive solutions for such semi-linear elliptic equations with small parameters are discussed.The existence of positive solutions is also discussed.The corresponding theorems are proved.As the application of theorems,an example is given.

关 键 词：不动点定理 半线性椭圆型方程 正解 

分 类 号：O175.6[理学—数学]