Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential

Abstract

In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth and a Hardy potential:under the assumptions that N ≥ 7, μ ∈ 0, (N −2) 2 4

Infinitely many solutions for quasilinear elliptic equations involving double critical terms and boundary geometry

“…This step will be disposed via index theory in case {c l } l is a finite set, see e.g. [6,7,15,17,27,33]. Both steps being confirmed implies that equation (1.1) admits infinitely many solutions.…”

“…In the following, we first illustrate the idea that will be used in this paper, and then give the main results of this paper. See also [6,7,33] for more applications of the same idea.…”

Uniqueness of positive radial solutions to singular critical growth quasilinear elliptic equations

“…For more results on existence of solutions to equation (1.1) and its variants, we refer to e.g. [4,7,8,9,16,17,18,21]. A very important ingredient in the argument of Han [18] is the following result, which was obtained by Abdellaoui, Felli and Peral [3] where C 1 , C 2 > 0 are constants depending only N, p and µ.…”

Infinitely many solutions for an elliptic Neumann problem involving critical Sobolev growth

“…Recently, there were a few results on the existence of infinitely many solutions for Dirichlet problem involving critical growth (see [9,10] for instance). On the other hand, it seems that there is no result on the existence of infinitely many solutions for Neumann problem with critical nonlinearities.…”