Multiple Solutions for a Class of System of (p, q)-Kirchhoff Equations in ℝN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{N}$\end{document}

被引:0
作者
Qiang Chen
Caisheng Chen
Yunfeng Wei
Yanling Shi
机构
[1] Yancheng Institute of Technology,School of Mathematics and Physics
[2] Hohai University,College of Science
[3] Nanjing Audit University,School of Statistics and Mathematics
关键词
(; , ; )-Kirchhoff system; Variational methods; Symmetric mountain pass theorem; Moser iteration; 35J20; 35J70; 35J92;
D O I
10.1007/s10883-020-09507-0
中图分类号
学科分类号
摘要
This paper is concerned with the (p, q)-Kirchhoff type equations, for which the existence of infinitely many high energy solutions is proved by employing the symmetric mountain pass lemma. Furthermore, an L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$L^{\infty }$\end{document} estimate for the solutions is given by applying the Moser iteration technique.
引用
收藏
页码:557 / 572
页数:15
相关论文
共 37 条
  • [1] Alves CO(2005)Positive solutions for a quasilinear elliptic equation of Kirchhoff type Comput Math Appl 49 85-93
  • [2] Correa FJSA(2015)Multiple solutions for nonhomogeneous schrödinger-kirchhoff type equations involving the fractional p-Laplacian in $\mathbb {R}^{N}$ℝN Calc Var Partial Differential Equations 54 2785-2806
  • [3] Ma TF(2009)Infinitely many positive solutions for Kirchhoff-type problems Nonlinear Anal 70 1407-1414
  • [4] Pucci P(2003)Positive solutions for a nonlinear nonlocal elliptic transmission problem Appl Math Lett 16 243-248
  • [5] Xiang M(2018)Combined effects for fractional Schrödinger-Kirchhoff systems with critical nonlinearities ESAIM:COCV 24 1249-1273
  • [6] Zhang B(2009)Sign-changing and multiple solutions of Kirchhoff type problems without the P.S.condition Nonlinear Anal 70 1275-1287
  • [7] He X(2006)Nontrival solutions of Kirchhoff-type problems via the Yang index J Differential Equations 221 246-255
  • [8] Zou W(2006)Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow J. Math. Anal. Appl. 317 456-463
  • [9] Ma TF(2012)Existence of a positive solution to Kirchhoff type problems without compactness conditions J Differential Equations 253 2285-2294
  • [10] Muñoz Rivera JE(2013)Multiple solutions for the nonhomogeneous Kirchhoff equation on $\mathbb {R}^{N}$ℝN Nonlinear Anal Real World Appl 14 1477-1486