Journal of Applied Mathematics
Volume 2013 (2013), Article ID 914210, 8 pages
http://dx.doi.org/10.1155/2013/914210
Research Article

Existence Results for a -Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition

Libo Wang1,2 and Minghe Pei2

1Institute of Mathematics, Jilin University, Chang'chun 130012, China
2Department of Mathematics, Beihua University, Ji'lin 132013, China

Received 25 November 2012; Accepted 28 April 2013

Academic Editor: Jaime Munoz Rivera

Copyright © 2013 Libo Wang and Minghe Pei. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the existence and multiplicity of solutions for the -Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many solutions were obtained, respectively.