Sign changing solution of the hardy-sobolev-maz'ya equation

TL;DR

This paper investigates the existence, multiplicity, and Morse index of sign-changing solutions for the Hardy-Sobolev-Maz'ya equation with critical growth in bounded domains, providing new insights into their properties.

Contribution

It establishes the existence of infinitely many sign-changing solutions and estimates their Morse index for the Hardy-Sobolev-Maz'ya equation with critical growth.

Findings

Infinitely many sign-changing solutions found.

Morse index estimates for solutions established.

Results contribute to understanding solution structure of HSM equations.

Abstract

In this article we will study the existence, multiplicity and Morse index of sign changing solutions for the Hardy-Sobolev-Maz'ya(HSM) equation in bounded domain and involving critical growth. We obtain infinitely many sign changing solutions for HSM equation. We also establish an estimate on the Morse index for the sign changing solutions.