Ground state solution for a class of supercritical Hénon equation with variable exponent

Abstract

This paper is concerned with the following supercritical Hénon equation with variable exponent $$ \begin{cases} -\Delta u=|x|^{\alpha}|u|^{2^*_\alpha-2+|x|^\beta}u&\text{in } B,\\ u=0 &\text{on } \partial B, \end{cases} $$% where $B\subset\mathbb{R}^N$ $(N\geq 3)$ is the unit ball, $\alpha\!> \!0$, $ 0\!< \!\beta\!< \!\min\{(N\!+\!\alpha)/2,N\!-\!2\}$ and $2^*_\alpha=({2N+2\alpha})/({N-2})$. We obtain the existence of positive ground state solution by applying the mountain pass theorem, concentration-compactness principle and approximation techniques.