MOUNTAIN-PASS SOLUTION FOR A KIRCHHOFF TYPE ELLIPTIC EQUATION  

作　　者：Lifu WENG Xu ZHANG Huansong ZHOU 翁立夫;张徐;周焕松

机构地区：[1]Center for Mathematical Sciences,Wuhan University of Technology,Wuhan,430070,China

出　　处：《Acta Mathematica Scientia》2025年第2期385-400,共16页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(11931012,11871387,12371118)。

摘　　要：We are concerned with a nonlinear elliptic equation,involving a Kirchhoff type nonlocal term and a potential V(x),onℝ3.As is well known that,even in,H_(r)^(1)(R^(3)),the nonlinear term is a pure power form of∣u∣^(p−1)u and V(x)≡1,it seems very difficult to apply the mountain-pass theorem to get a solution(i.e.,mountain-pass solution)to this kind of equation for all p∈(1,5),due to the difficulty of verifying the boundedness of the PalaisSmale sequence obtained by the mountain-pass theorem when p∈(1,3).In this paper,we find a new strategy to overcome this difficulty,and then get a mountain-pass solution to the equation for all p∈(1,5)and for both V(x)being constant and nonconstant.Also,we find a possibly optimal condition on V(x).

关 键 词：elliptic equation ground state mountain-pass solution Kirchhoff equation 

分 类 号：O175.25[理学—数学]