Analysis of degenerate p-Laplacian elliptic equations involving Hardy terms: Existence and numbers of solutions

This article investigates the existence of solutions to quasilinear degenerate elliptic equation with Hardy singular coefficient, in which the weighted function $\omega \left(x\right)$ is unbounded (singular), then we cannot use the classical space $W_0^{1,p}\left(\Omega \right)$, so we have to find another space $W_0^{1,p}(\omega ,\Omega )$ to deal with the difficulties caused by singularities or degeneracies. New criteria for the existence of at least one and at least two generalized solutions are established via variational methods and critical point theorems provided that the nonlinearity satisfies appropriate hypotheses.