Concentration estimates and multiple solutions to elliptic problems at critical growth

Abstract

In this paper, we consider the problem -Δu = |u|2*-2u+λu in ω, u = 0 on ∂ω, where ω is an open regular bounded subset of ℝN (N ≥3), 2* = 2N/N-2 is the critical Sobolev exponent and λ> 0. Our main result asserts that, if N ≥7, the problem has infinitely many solutions and, from the point of view of the compactness arguments employed here, the restriction on the dimension N cannot be weakened.