Fractional Sobolev-Choquard critical systems with Hardy term and weighted singularities

TL;DR

This paper investigates a fractional p-Laplacian system with complex singular nonlinearities, including Hardy and Choquard critical terms, establishing existence conditions for solutions using advanced inequalities and variational methods.

Contribution

It introduces new existence results for fractional systems with doubly critical singularities and weights, employing refined Sobolev and Caffarelli-Kohn-Nirenberg inequalities.

Findings

Existence of weak nontrivial solutions under certain conditions

Development of refined inequalities for doubly critical exponents

Application of variational methods to complex fractional systems

Abstract

In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem also includes a homogeneous singular Hardy term; moreover, all the nonlinearities involve singular critical weights. To prove the main result we use a refinement of Sobolev inequality that is related to Morrey space because our problem involves doubly critical exponentss and a version of the Caffarelli-Kohn-Nirenberg inequality. With the help of these results, we provide sufficient conditions under which a weak nontrivial solution to the problem exists via variational methods.