Nonlocal fourth-order Kirchhoff systems with variable growth: low and high energy solutions

被引：0
作者：
Ghasem A. Afrouzi
M. Mirzapour
Vicenţiu D. Rădulescu
机构：
[1] University of Mazandaran,Department of Mathematics, Faculty of Mathematical Sciences
[2] Farhangian University,Department of Mathematics, Faculty of Sciences
[3] King Abdulaziz University,undefined
[4] Institute of Mathematics “Simion Stoilow” of the Romanian Academy,undefined
来源：
Collectanea Mathematica | 2016年 / 67卷
关键词：
Variational method; Nonlinear elliptic systems; -Kirchhoff system; Nonlocal condition; 35J60; 35B30; 35B40; 58E05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with the existence and multiplicity of solutions for a class of nonlocal fourth-order (p(x),q(x))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p(x),q(x))$$\end{document}-Kirchhoff systems. By means of a variational analysis, we obtain conditions for the existence of infinitely many solutions with high (resp., low) energies. The arguments combine related critical point theory arguments with a careful analysis of the energy levels.
引用
收藏
页码：207 / 223
页数：16
相关论文
共 46 条
[1]  
Alves CO(2012)Nonlinear perturbations of a periodic Kirchhoff equation in Nonlinear Anal. 75 2750-2759
[2]  
Figueiredo G(1973)Dual variational methods in critical point theory and applications J. Funct. Anal. 14 349-381
[3]  
Ambrosetti A(2009)Existence of solutions for fourth-order PDEs with variable exponents Electron. J. Differ. Equ. 153 1-13
[4]  
Rabinowitz PH(2006)Elliptic equations and systems with nonstandard growth conditions: existence, uniqueness, localization properties of solutions Nonlinear Anal. 65 728-761
[5]  
El Amrouss A(2010)Kirchhoff systems with nonlinear source and boundary damping terms Commun. Pure Appl. Anal. 9 1161-1188
[6]  
Moradi F(2010)Kirchhoff systems with dynamic boundary conditions Nonlinear Anal. 73 1952-1965
[7]  
Moussaoui M(2011)Local asymptotic stability for polyharmonic Kirchhoff systems Appl. Anal. 90 493-514
[8]  
Antontsev S(2010)Global nonexistence for nonlinear Kirchhoff systems Arch. Rational Mech. Anal. 196 489-516
[9]  
Shmarev S(1993)Infinitely many solutions of a symmetric Dirichlet problem Nonlinear Anal. 20 1205-1216
[10]  
Autuori G(1940)Sur une classe d’équations fonctionnelles aux dérivées partielles (in Russian with French summary) Bull. Acad. Sci. URSS, Set Math. 4 17-26
12345