Existence, stability and oscillation properties of slow decay positive solutions of supercritical elliptic equations with Hardy potential

TL;DR

This paper investigates the existence, stability, and oscillation characteristics of slow decay positive solutions to supercritical elliptic equations with Hardy potential, including solutions in the entire space and exterior domains.

Contribution

It establishes the existence of a family of slow decay solutions and analyzes their stability and oscillation properties, extending understanding of such solutions in supercritical elliptic equations.

Findings

Existence of a family of slow decay positive solutions in the entire space.

Identification of stability and oscillation properties of these solutions.

Existence of a continuum of stable solutions for exterior Dirichlet problems.

Abstract

We prove the existence of a family of slow decay positive solutions of a supercritical elliptic equation with Hardy potential in the entire space and study stability and oscillation properties of these solutions. We also establish the existence of a continuum of stable slow decay positive solutions for the relevant exterior Dirichlet problem.