有界洞型区域内半线性椭圆型方程组的正解  

Positive Solutions to Semilinear Elliptic Systems in a Bounded Domain with a Hole

作　　者：周子豪 钟金标 ZHOU Zihao;ZHONG Jinbiao(School of Mathematics 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）》2023年第1期16-21,共6页Journal of Anqing Normal University(Natural Science Edition)

摘　　要：本文在有界洞型区域内,讨论了带有第一边界条件的一类半线性椭圆型方程组的可解性。此方程组各方程中未知函数均包含了线性部分与非线性部分,通过将方程组边值问题转换为向量方程边值问题后,再利用不动点定理、Green第一恒等式和Poincare不等式等理论方法证明了正解的存在性,同时讨论了在一定条件下解的唯一性。本文分别给出了正解存在性和正解唯一性的两个具体定理应用实例。In this paper,the solvability of a class of semilinear elliptic systems with first boundary condition are discussed in a bounded domain with a hole.Each equation in this system have contained linear part and nonlinear part about unknown functions.The existence of positive solutions has been proved by using the fixed-point theorem,Green’s first identity,Poincare inequality and other theoretical methods after systems boundary problems are transformed into vector equations boundary problems.Also,under certain conditions,the uniqueness of solution is discussed.As an application of the main theorem,two specific examples of the existence and uniqueness of positive solutions are given.

关 键 词：正解 不动点定理 紧正算子 Green第一恒等式 POINCARE不等式 

分 类 号：O175.25[理学—数学]