Existence of solutions for a singular double phase problem involving a $\psi$-Hilfer Fractional operator via Nehari Manifold

TL;DR

This paper establishes the existence of multiple solutions for a singular double phase p-Laplacian problem involving a $$-Hilfer fractional operator, using the Nehari manifold and fibering method.

Contribution

It introduces a new class of singular double phase problems with a $$-Hilfer fractional operator and proves the existence of multiple solutions via variational methods.

Findings

Existence of at least two weak solutions for small parameters.

Development of energy functional and Nehari manifold analysis.

Application of fibering method to fractional double phase problems.

Abstract

In this present paper, we investigate a new class of singular double phase $p$-Laplacian equation problems with a $\psi$-Hilfer fractional operator combined from a parametric term. Motivated by the fibering method using the Nehari manifold, we discuss the existence of at least two weak solutions to such problems when the parameter is small enough. Before attacking the main contribution, we discuss some results involving the energy functional and the Nehari manifold.