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Multiplicity of high energy solutions for superlinear Kirchhoff equations

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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.

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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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  1. College of Science, Minzu University of China, Beijing, 100081, P.R. China

    Wei Liu & Xiaoming He

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  1. Wei Liu
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  2. Xiaoming He
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Correspondence to Wei Liu or Xiaoming He.

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Liu, W., He, X. Multiplicity of high energy solutions for superlinear Kirchhoff equations. J. Appl. Math. Comput. 39, 473–487 (2012). https://doi.org/10.1007/s12190-012-0536-1

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