Sign changing solutions of the Hardy–Sobolev–Maz'ya equation

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.

Keywords

• hardy–sobolev–maz'ya equation
• sign changing solutions
• morse index
• 35j20
• 35j60
• 35b33