Electron. J. Diff. Equ., Vol. 2015 (2015), No. 84, pp. 1-11.

Ground state solutions for semilinear elliptic equations with zero mass in R^N

Jiu Liu, Jia-Feng Liao, Chun-Lei Tang

Abstract:
In this article, we study the semilinear elliptic equation
$$\displaylines{ -\Delta u=|u|^{p(x)-2}u, \quad x\in \mathbb{R}^N\cr u\in D^{1,2}(\mathbb{R}^N), }$$
where $N\geq3$, $p(x)= p$ if $x \in\Omega$, and $p(x)=2^*:=2N/(N-2)$ if $x\not\in\Omega$, where $\Omega\subset\mathbb{R}^N$ is a bounded set with nonempty interior. By using the Nehari manifold, we obtain a positive ground state solution.

Submitted January 17, 2015. Published April 7, 2015.
Math Subject Classifications: 35J20, 35J61.
Key Words: Semilinear elliptic equation; zero mass; Nehari manifold; ground state solution.

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Jiu Liu
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: jiuliu2011@163.com
Jia-Feng Liao
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: liaojiafeng@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

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