Ground state solution for a class of supercritical Hénon equation with variable exponent - Feng, Xiaojing (Topological Methods in Nonlinear Analysis, 2023)
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.