Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension

Abstract

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.

Keywords

• strong singularity
• critical nonlinearity
• non-local operator
• subcritical perturbation
• topology of sublevels
• Szulkin functional