Journal of Applied Mathematics and Computing

, Volume 39, Issue 1, pp 473–487

Multiplicity of high energy solutions for superlinear Kirchhoff equations

Original Research

DOI: 10.1007/s12190-012-0536-1

Cite this article as:
Liu, W. & He, X. J. Appl. Math. Comput. (2012) 39: 473. doi:10.1007/s12190-012-0536-1


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.


Nonlinear Kirchhoff equationsHigh energy solutionsVariational methods

Mathematics Subject Classification (2000)


Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

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