Existence and multiplicity of weak solutions for a nonlinear impulsive (q,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(q,p)$\end{document}-Laplacian dynamical system

被引：0
作者：
Xiaoxia Yang
机构：
[1] Central South University,School of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2017卷 / 1期
关键词：
-Laplacian; existence; multiplicity; nontrivial solution; variational methods; 34C25; 58E50;
D O I：
10.1186/s13662-017-1145-y
中图分类号：
学科分类号：
摘要：
In this paper, we investigate the existence and multiplicity of nontrivial weak solutions for a class of nonlinear impulsive (q,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(q,p)$\end{document}-Laplacian dynamical systems. The key contributions of this paper lie in (i) Exploiting the least action principle, we deduce that the system we are interested in has at least one weak solution if the potential function has sub-(q,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(q,p)$\end{document} growth or (q,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(q,p)$\end{document} growth; (ii) Employing a critical point theorem due to Ding (Nonlinear Anal. 25(11):1095-1113, 1995), we derive that the system involved has infinitely many weak solutions provided that the potential function is even.
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