Infinitely many solutions for fractional elliptic systems involving critical nonlinearities and Hardy potentials

Abstract

This paper is dedicated to studying the existence of multiple nontrivial solutions for a class of singular fractional elliptic systems involving critical nonlinearities and Hardy potentials in RN. Based upon the Caffarelli–Silvestre extension method and the Krasnoselskii genus theory, together with the symmetric criticality principle of Palais, we establish several existence results of infinitely many solutions under certain appropriate hypotheses on the weights and the parameters.

Keywords

• Infinitely many solutions
• Critical Sobolev exponent
• Fractional Hardy inequality
• Fractional elliptic system