Electron. J. Diff. Equ., Vol. 2015 (2015), No. 262, pp. 1-14.

Positive ground state solution for Kirchhoff equations with subcritical growth and zero mass

Yu Duan, Jiu Liu, Chun-Lei Tang

Abstract:
In this article, we study the Kirchhoff equation
$$\displaylines{ -\Big(a+b\int_{\mathbb{R}^N}|\nabla u|^{2}dx\Big)\Delta u=K(x)f(u), \quad x\in \mathbb{R}^N,\cr u\in D^{1,2}(\mathbb{R}^N), }$$
where $a>0$, $b>0$ and $N\geq3$. Under suitable conditions on K and f, we obtain four existence results and two nonexistence results, using variational methods.

Submitted September 7, 2015. Published October 8, 2015.
Math Subject Classifications: 35J20, 35J60, 35A01.
Key Words: Kirchhoff equation; subcritical growth; zero mass; Pohozaev identity.

Show me the PDF file (272 KB), TEX file, and other files for this article.

Yu Duan
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: duanyu3612@163.com
Jiu Liu
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: jiuliu2011@163.com
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
Phone +86 23 68253135, Fax +86 23 68253135
email: tangcl@swu.edu.cn

Return to the EJDE web page