Existence results for elliptic problems with Hardy potential

In this work we obtain existence results for some singular elliptic Dirichlet problems involving the p-Laplacian. Precisely, starting from a weak lower semicontinuity result and by using the classical Hardy inequality, a critical point result for differentiable functionals is exploited, in order to prove the existence of a precise open interval of positive eigenvalues for which the treated problems admit at least one non-trivial weak solution.