Existence, non-existence and regularity of radial ground states for p-Laplacian equations with singular weights

Abstract

By the Mountain Pass Theorem and the constrained minimization method existence of positive or compactly supported radial ground states for quasilinear singular elliptic equations with weights are established. The paper also includes the discussion of regularity and the validity of useful qualitative properties of the solutions, which seems of independent interest. Finally, a Pohozaev type identity is produced to deduce some non-existence results.