Semilinear elliptic equations involving fractional Hardy operators

TL;DR

This paper investigates semilinear elliptic equations with fractional Hardy operators, analyzing existence and uniqueness under various conditions involving potentials, absorption, and measure concentration.

Contribution

It provides new existence and uniqueness results for equations involving fractional Hardy operators with complex interactions.

Findings

Existence of solutions under certain growth conditions.

Uniqueness results for specific parameter ranges.

Analysis of measure concentration effects.

Abstract

Our aim in this article is to study semilinear elliptic equations involving a fractional Hardy operator, an absorption and a Radon source in a weighted distributional sense. We show various scenarios, produced by the combined effect of the fractional Hardy potential, the growth of the absorption term and the concentration of the measure, in which existence and uniqueness results holds.