Abstract
The aim of this paper is to prove the existence of multiple positive solutions to the following critical p–Laplacian system with singular potential [Formula: see text] where Ω is a starshaped bounded domain of ℝNwith respect to the origin, p* and q* denote the critical Sobolev exponents and the parameters λ, α, β and γ satisfy some mild conditions. Our system corresponds to a perturbed critical problem which has no positive solutions (λ = 0). We show that the form of the associated energy functional has a local property and satisfies the requirements of the Mountain–Pass geometry; then the Ekeland variational principle and the concept of Palais–Smale sequences will be useful.
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