Infinitely Many Sign-Changing Solutions for Kirchhoff-Type Equations in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3$$\end{document}

被引:0
作者
Dongdong Qin
Fangfang Liao
Yubo He
Xianhua Tang
机构
[1] Central South University,School of Mathematics and Statistics
[2] Xiangnan University,Department of Mathematics
[3] Huaihua University,Department of Mathematic and Applied Mathematics
关键词
Kirchhoff-type equations; Variational method; Sign-changing solutions; Invariant sets of descent flow; 35J20; 35J60;
D O I
10.1007/s40840-017-0534-4
中图分类号
学科分类号
摘要
Employing the minimax method incorporated with invariant sets of descending flow, we prove some results about the existence of sign-changing solutions for a class of Kirchhoff-type equation. In particular, a sequence of high-energy sign-changing solutions is obtained.
引用
收藏
页码:1055 / 1070
页数:15
相关论文
共 78 条
[1]  
Al-Gwaiz M(2014)Bending and stretching energies in a rectangular plate modeling suspension bridges Nonlinear Anal. 106 18-34
[2]  
Benci V(1996)On the well-posedness of the Kirchhoff string Trans. Am. Math. Soc. 348 305-330
[3]  
Gazzola F(2004)On a superlinear elliptic p-Laplacian equation J. Differ. Equ. 198 149-175
[4]  
Arosio A(2005)Nodal solutions of a p-Laplacian equation Proc. Lond. Math. Soc. 91 129-152
[5]  
Panizzi S(1983)Nonlinear scalar field equations. I. Existence of ground state Arch. Ration. Mech. Anal. 82 313-345
[6]  
Bartsch T(1983)Positive solutions of nonlinear elliptic equations involving critical exponents Commun. Pure Appl. Math. 36 437-477
[7]  
Liu Z(2011)The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions J. Differ. Equ. 250 1876-1908
[8]  
Bartsch T(1997)Some remarks on nonlocal elliptic and parabolic problems Nonlinear Anal. 30 4619-4627
[9]  
Liu Z(2004)On positive solutions of nonlocal and nonvariational elliptic problems Nonlinear Anal. 59 1147-1155
[10]  
Weth T(2015)Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in J. Funct. Anal. 269 3500-3527