POSITIVE SOLUTIONS FOR A KIRCHHOFF EQUATION WITH PERTURBED SOURCE TERMS  

作　　者：Narimane AISSAOUI Wei LONG Narimane AISSAOUI;龙薇(School of Mathematics and Statistics,Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China;College of Mathematics and Information Science,Jiangci Normal University,Nanchang 330022,China)

机构地区：[1]School of Mathematics and Statistics,Hubei Key Laboratory of Mathematical Sciences,Central China Normal University,Wuhan 430079,China [2]College of Mathematics and Information Science,Jiangci Normal University,Nanchang 330022,China

出　　处：《Acta Mathematica Scientia》2022年第5期1817-1830,共14页数学物理学报（B辑英文版）

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).

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),u>0,x∈R^(3),u∈H^(1)(R^(3)).Here a,b are positive constants,V(x),Q(x)are positive radial potentials,1<p<5,ε>0 is a small parameter,f(x)is an external source term in L^(2)(R^(3))∩L^(∞)(R^(3)).

关 键 词：nonlinear Kirchhoff problem Lyapunov-Schmidt reduction positive solutions level set 

分 类 号：O175[理学—数学]