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 

Notes

Acknowledgements

The authors are grateful for the anonymous referees for very helpful suggestions and comments. This work was supported by NSFC Grants 10971238 and the Fundamental Research Funds for the Central Universities 0910KYZY51.

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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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