Ground state solutions for p-biharmonic equations

• Main Authors: Xiaonan Liu, Haibo Chen, Belal Almuaalemi
• Format: Article
• Language: English
• Published: Texas State University 2017-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: p-biharmonic equations; Nehari manifold; ground state solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/45/abstr.html

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.