A perturbed nonlinear elliptic PDE with two Hardy–Sobolev critical exponents

Abstract

Let [Formula: see text] be a [Formula: see text] open bounded domain in [Formula: see text] ([Formula: see text]) with [Formula: see text]. Suppose that [Formula: see text] is [Formula: see text] at [Formula: see text] and the mean curvature of [Formula: see text] at [Formula: see text] is negative. Consider the following perturbed PDE involving two Hardy–Sobolev critical exponents: [Formula: see text] where [Formula: see text]. The existence of ground state solution is studied under different assumptions via the concentration compactness principle and the Nehari manifold method. We also apply a perturbation method to study the existence of positive solution.