Existence of solutions to fractional p-Laplacian problems with Robin boundary conditions

This article studies the existence of solutions for the fractional p-Laplacian problem $$\displaylines{(-\Delta)_p^su=\lambda|u|^{q-2}u+ \frac{|u|^{r-2}u}{|x|^\alpha},\quad \hbox{in } \Omega,\cr{N}_{s,p}u(x)+\beta(x)|u|^{p-2}u=0, \quad\hbox{in }\mathbb{R}^n\backslash\Omega,}$$ where \(\Omega\) is a smooth bounded domain in \({\mathbb{R}}^n\) containing \(0\) with smooth boundary, \((-\Delta)_p^s\) denotes the fractional p-Laplace operator and \(\lambda>0\), \(1<q<p<r<p_\alpha^*\), \(p_\alpha^*\) is the fractional critical Hardy-Sobolev exponent for \(0\leq \alpha<ps<n\) and \(0<s<1\). By using fibering maps and Nehari manifold, we obtain the existence of solution for Hardy-Sobolev subcritical and critical cases. For more information see https://ejde.math.txstate.edu/Volumes/2025/13/abstr.html