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

被引：371

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

页码：1275 / 1287

页数：13

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