Weak linking theorems and Schrodinger equations with critical Sobolev exponent

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 Schrodinger equation - Deltau + V (x) u = K(x) \u\(2*-2) u+ g(x, u); u is an element of W-1,W-2(R-N), where N greater than or equal to 4; V; K; g are periodic in x(j) for 1 less than or equal to j less than or equal to N and 0 is in a gap of the spectrum of - + V; K > 0. If 0 < g(x; u) u <= c\u\(2*) for an appropriate constant c, we show that this equation has a nontrivial solution.