非线性椭圆型方程组边值问题的可解性  

Solvability of Boundary Value Problems for Nonlinear Elliptic Equations

作　　者：李殷杰 钟金标 LI Yinjie;ZHONG Jinbiao(School of Mathematics and Physics,Anqing Normal University,Anqing Anhui 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《大学数学》2023年第5期1-4,共4页College Mathematics

摘　　要：研究椭圆型方程组Dirichlet边值问题的可解性,利用不动点定理证明了上述问题存在上、下解情形,存在有界非负解,并利用该结论讨论了带参数的椭圆型方程组Dirichlet边值问题通过寻找该问题的上、下解,证明了正参数充分小时,这个问题存在有界正解.这里非线性函数在+∞处可以是超线性的,从而证明了部分椭圆型方程组边值问题中非线性项为超线性时,有界正解的存在性.同时,作为定理的应用,给出了实例.We study the solvability of the Dirichlet boundary value problem of the elliptic equations.By using the fixed point theorem,we prove that there are upper and lower solutions and the existence of bounded nonnegative solutions to the above problems.By using this conclusion,we discuss the Dirichlet boundary value problem of elliptic equations with parameters.When positive parametes is sufficiently small,there is a bounded positive solution to this problem.Here the nonlinear functions can be superlinear at positive infinity,which proves the existence of a bounded positive solution when the nonlinear term is superlinear in the boundary value problems of partially elliptic equation systems.At the same time,as an application of the theorem,an example is given.

关 键 词：紧正算子 确界原理 SCHAUDER不动点定理 HOLDER连续 

分 类 号：O175[理学—数学]