On nonhomogeneous elliptic equations with the Hardy-Leray potentials

TL;DR

This paper investigates solutions to nonhomogeneous elliptic equations with Hardy-Leray potentials, establishing distributional identities and exploring qualitative properties, nonexistence results, and eigenvalue principles related to these equations.

Contribution

It introduces new distributional identities for solutions and applies them to analyze nonexistence and eigenvalue problems involving Hardy-Leray potentials.

Findings

Distributional identities for solutions

Nonexistence results for certain problems

Nonexistence principle for eigenvalues with indefinite potentials

Abstract

In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities. We address some applications on the nonexistence of some nonhomogeneous problems with the Hardy-Leray potentials and the nonexistence principle eigenvalue with some indefinite potentials.