MULTIPLICITY RESULT FOR CRITICAL P-LAPLACIAN SYSTEMS WITH SINGULAR POTENTIAL

The aim of this paper is to prove the existence of multiple positive solutions to the following critical pLaplacian system with singular potential [GRAPHIC] where Omega is a starshaped bounded domain of R-N with respect to the origin, p* and q* denote the critical Sobolev exponents and the parameters lambda, alpha, beta and gamma satisfy some mild conditions. Our system corresponds to a perturbed critical problem which has no positive solutions (lambda = 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.