Multiplicity of high energy solutions for superlinear Kirchhoff equations

Original Research

Abstract

In this paper, we study the existence of infinitely many high energy solutions for the nonlinear Kirchhoff equations
$$\left\{\everymath{\displaystyle}\begin{array}{l@{\quad}l}- \biggl(a+b\int_{R^3} |\nabla u|^2 dx\biggr)\Delta u + V(x)u=f(x,u),&x\in \mathbb {R}^3,\\[9pt]u\in H^1 (\mathbb {R}^3),\end{array}\right.$$
where a,b>0 are constants, V:ℝ3→ℝ is continuous and has a positive infimum. f is a subcritical nonlinearity which needs not to satisfy the usual Ambrosetti-Rabinowitz-type growth conditions.

Keywords

Nonlinear Kirchhoff equations High energy solutions Variational methods 

Mathematics Subject Classification (2000)

35J60 35J25 

Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.College of ScienceMinzu University of ChinaBeijingP.R. China

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