Electron. J. Differential Equations, Vol. 2017 (2017), No. 45, pp. 1-9.

Ground state solutions for p-biharmonic equations

Xiaonan Liu, Haibo Chen, Belal Almuaalemi

Abstract:
In this article we study the p-biharmonic equation
$$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$
where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator. When V(x) and f(x,u) satisfy some conditions, we prove that the above equations have Nehari-type ground state solutions.

Submitted November 10, 2016. Published February 14, 2017.
Math Subject Classifications: 35B38, 35G99.
Key Words: p-biharmonic equations; Nehari manifold; ground state solution.

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Xiaonan Liu
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: liuxiaonan20131110@163.com
Haibo Chen
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: math_chb@csu.edu.cn
Belal Almuaalemi
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: Belal_cn1980@hotmail.com

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