POSITIVE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH PERTURBED SOURCE TERMS

作     者：Narimane AISSAOUI 龙薇 Narimane AISSAOUI;Wei LONG

作者机构：School of Mathematics and StatisticsHubei Key Laboratory of Mathematical SciencesCentral China Normal UniversityWuhan 430079China College of Mathematics and Information ScienceJiangci Normal UniversityNanchang 330022China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第5期

页      面：1817-1830页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by NSF of China(11871253) supported by Jiangxi Provincial Natural Science Foundation(20212ACB201003) Jiangxi Two Thousand Talents Program(jxsq2019101001) Double-high talents in Jiangxi Province and Jiangxi Provincial Department of Education Fund(GJJ191687). 

主　　题：nonlinear Kirchhoff problem Lyapunov-Schmidt reduction positive solutions level set 

摘      要：This paper deals with the existence of positive solutions to the following nonlinear Kirchhoff equation with perturbed external source terms:{−(a+b∫_(R^(3))|∇u|^(2)dx)Δu+V(x)u=Q(x)u^(p)+εf(x),u0,x∈R^(3),u∈H^(1)(R^(3)).Here a,b are positive constants,V(x),Q(x)are positive radial potentials,10 is a small parameter,f(x)is an external source term in L^(2)(R^(3))∩L^(∞)(R^(3)).