一类带对数的半线性椭圆方程的多解  

Multiple Solutions for A Class of Semilinear Elliptic Equations with Logarithmic Nonlinearity

作　　者：李雨涵 廖家锋 LI Yu-han;LIAO Jia-feng(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2024年第6期595-599,共5页Journal of China West Normal University(Natural Sciences)

基　　金：四川省自然科学基金项目(2023NSFSC0073)。

摘　　要：本文研究了有界区域上一类带对数非线性项的半线性椭圆方程多解的存在性。首先,在Nehari流形上利用变分法证明该方程存在一个能量为负的正基态解;其次,证明问题对应的能量泛函满足(PS)条件,再借助Clark定理得到该问题的一列解。该结论在一定程度上补充完善了近期相关结果。This paper talks about the existence of multiple solutions for a class of semilinear elliptic equations with logarithmic nonlinearity on a bounded domain.Firstly,the variational method is employed to prove the existence of a positive ground state solution on Nehari manifold,which has negative energy.Secondly,it is proved that the corresponding energy functional satisfies the(PS)condition.Then,a sequence of solutions are obtained by the Clark's Theorem.The conclusion has complemented and improved the recent relevant results to some extent.

关 键 词：对数非线性 变分法 NEHARI流形 多解 

分 类 号：O177.91[理学—数学]