Multiplicity of Solutions for an Elliptic Problem with Critical Sobolev-Hardy Exponents and Concave-Convex Nonlinearities

Abstract EN

We study the existence of multiple solutions for the following elliptic problem: - Δ p u - μ | u | p - 2 u / | x | p = | u | p * ( t ) - 2 / | x | t u + λ | u | q - 2 / | x | s u , u ∈ W 0 1 , p ( Ω ) .

We prove that if 1 ≤ q < p < N , then there is a μ 0 , such that for any μ ∈ 0 , μ 0 , the above mentioned problem possesses infinitely many weak solutions.

Our result generalizes a similar result (Azorero and Alonso, 1991).