Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities

TL;DR

This paper investigates the existence of nontrivial solutions for a complex fractional p-Kirchhoff equation with multiple nonlinearities and singular weights, employing advanced variational methods to overcome compactness challenges.

Contribution

It advances the study of fractional p-Kirchhoff equations by establishing existence results under more general nonlinearities and singular weights using the Cerami condition.

Findings

Existence of nontrivial weak solutions proven.

Handling of critical singular weights and nonlocal terms.

Use of Cerami condition to address compactness issues.

Abstract

In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem also includes a Hardy-type term; additionaly, all terms have critical singular weights. Our result improve upon previous work in the following ways: we focus our attention on the existence of a nontrivial weak solution for fractional p-Kirchhoff equation in the entire space R^N. The possibility of a slower growth in the nonlinearity makes it more difficult to establish a compactness condition; to do so, we use the Cerami condition. The crucial points in our argument are the uniform boundedness of the convolution part and the lack of compactness of the Sobolev embeddings.