A variational approach to nonlocal singular problems

TL;DR

This paper introduces a variational method to address nonlocal problems with fractional Laplacian and singular nonlinearities, overcoming limitations of traditional techniques and providing a way to characterize solutions.

Contribution

It develops a novel variational framework specifically designed for nonlocal singular problems involving the fractional Laplacian.

Findings

Established a variational approach for fractional Laplacian problems with singular nonlinearities.

Derived a characterization of solutions within this new framework.

Overcame limitations of standard methods for these complex problems.

Abstract

We provide a suitable variational approach for a class of nonlocal problems involving the fractional laplacian and singular nonlinearities for which the standard techniques fail. As a corollary we deduce a characterization of the solutions.