Electron. J. Diff. Equ., Vol. 2015 (2015), No. 47, pp. 1-8.

Existence of solutions for Kirchhoff type equations

Qi-Lin Xie, Xing-Ping Wu, Chun-Lei Tang

Abstract:
In this article, we prove the existence of solutions for Kirchhoff type equations with Dirichlet boundary-value condition. We use the Mountain Pass Theorem in critical point theory, without the (PS) condition.

Submitted August 13, 2014. Published February 17, 2015.
Math Subject Classifications: 35J60, 47J30, 35J20.
Key Words: Kirchhoff type equation; Dirichlet problem; critical point; Mountain Pass Theorem.

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Qi-Lin Xie
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: xieqilinsxdt@163.com
Xing-Ping Wu
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: wuxp@swu.edu.cn
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: tangcl@swu.edu.cn, tangcl8888@sina.com

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