Existence and H\"{o}lder regularity of infinitely many solutions to a $p$-Kirchhoff type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition

TL;DR

This paper proves the existence of infinitely many solutions for a fractional p-Kirchhoff problem with singularities and superlinear nonlinearity, establishing their boundedness and regularity without the AR condition.

Contribution

It demonstrates the existence of infinitely many solutions to a fractional p-Kirchhoff problem involving singularities and superlinear terms, without relying on the AR condition.

Findings

Solutions are bounded and possess Hölder regularity.

A weak comparison principle is established.

Analysis includes $C^1$ versus $W_0^{s,p}$ regularity comparison.

Abstract

We carry out an investigation of the existence of infinitely many solutions to a fractional $p$-Kirchhoff type problem with a singularity and a superlinear nonlinearity with a homogeneous Dirichlet boundary condition. Further the solution(s) will be proved to be bounded and a weak comparison principle has also been proved. A {\it `$C^1$ versus $W_0^{s,p}$'} analysis has also been discussed.