Positive weak solutions of a double-phase variable exponent problem with a fractional-Hardy-type singular potential and superlinear nonlinearity

TL;DR

This paper establishes the existence of positive weak solutions for a complex double-phase variable exponent problem involving a fractional-Hardy-type singular potential and superlinear nonlinearity, using variational methods.

Contribution

It introduces a novel approach combining the Mountain-Pass theorem and strong minimum principle to handle singular potentials in variable exponent problems.

Findings

Existence of at least one positive weak solution is proven.

The problem involves a fractional-Hardy-type singular potential.

Variational methods are effectively applied to a double-phase variable exponent setting.

Abstract

In the present paper, we study a double-phase variable exponent problem which is set up within a variational framework including a singular potential of fractional-Hardy-type. We employ the Mountain-Pass theorem and the strong minimum principle to obtain the existence of at least one nontrivial positive weak solution.