Weak linking theorems and schrödinger equations with critical Sobolev exponent

Abstract

In this paper we establish a variant and generalized weak linking theorem, which contains more delicate result and insures the existence of bounded Palais-Smale sequences of a strongly indefinite functional. The abstract result will be used to study the semilinear Schrödinger equation −Εu + V(x)u = K(x)|u|2*−2u+g(x, u), u ∈ W1,2(RN), where N ≥ 4; V, K, g are periodic in xj for 1≤j≤N and 0 is in a gap of the spectrum of −Ε+ V ; K>0. If 0