Mountain pass solution to a perturbated Hardy–Sobolev equation involving p-Laplacian on compact Riemannian manifolds

Abstract

ABSTRACT In this paper, we consider the following quasilinear equation: where M is a compact Riemannian manifold with dimension without boundary, and . Here , and are continuous functions on M satisfying some further conditions. The operator is the p-Laplace–Beltrami operator on M associated with the metric g, and is the Riemannian distance on . Moreover, we assume , , and with . The notion is the critical Hardy–Sobolev exponent. With the help of Mountain Pass Theorem, we get the existence results under different assumptions.