Multiple sign-changing solutions for Kirchhoff-type equations in R3

被引：3

作者：

He, Xiumei ^{[1
]}

Wu, Xian ^{[2
]}

机构：

[1] Kunming Univ, Dept Math, Kunming 650214, Yunnan, Peoples R China

[2] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff-type equations; critical point theorem; sign-changing solutions; HIGH-ENERGY SOLUTIONS; POSITIVE SOLUTIONS; NONTRIVIAL SOLUTIONS; EXISTENCE;

D O I：

10.1002/mma.4346

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following Kirchhoff-type equations -(a+b integral(R3) vertical bar del u vertical bar(2)dx) Delta u + V(x)u = vertical bar u vertical bar(p-2)u, x is an element of R-3, where a > 0, b >= 0, 4 < p < 2* = 6, and V is an element of C(R-3, R). Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, this problem has infinitely many sign-changing solutions. Copyright (c) 2017 John Wiley & Sons, Ltd

引用

页码：512 / 524

页数：13

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