Sign-changing and multiple solutions of Kirchhoff type problems without the PS condition

被引：372
作者：
Mao, Anmin [2 ]
Zhang, Zhitao [1 ]
机构：
[1] Chinese Acad Sci, Inst Math, Beijing 100080, Peoples R China
[2] Qufu Normal Univ, Dept Math, Qufu 273165, Shandong, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Critical points; Sign-changing solutions and multiple solutions; Kirchhoff type nonlocal problems; BOUNDARY-VALUE-PROBLEMS; SCHRODINGER-EQUATION; NONTRIVIAL SOLUTION; HAMILTONIAN SYSTEM; POSITIVE SOLUTIONS; INVARIANT-SETS; EXISTENCE; FLOW;
D O I：
10.1016/j.na.2008.02.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The existence of nontrivial solutions of Kirchhoff type equations is an important nonlocal quasilinear problem; in this paper we use minimax methods and invariant sets of descent flow to prove two interesting existence theorems for the following 4-superlinear Kirchhoff type problems without the P.S. condition, one concerning the existence of a nontrivial solution and the other one concerning the existence of sign-changing Solutions and multiple solutions, {-(a + b integral(Omega)\del u\(2))Delta u = f(x, u) in Omega, on partial derivative Omega. u = 0 (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1275 / 1287
页数：13
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