Infinitely many sign-changing solutions for the brézis-nirenberg problem involving hardy potential

In this article, we give a new proof on the existence of infinitely many sign-changing solutions for the following Brézis-Nirenberg problem with critical exponent and a Hardy potential where Ω is a smooth open bounded domain of which contains the origin, is the critical Sobolev exponent. More precisely, under the assumptions that , and , we show that the problem admits infinitely many sign-changing solutions for each fixed λ > 0. Our proof is based on a combination of invariant sets method and Ljusternik-Schnirelman theory.