Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent
Martin Schechter, Wenming Zou (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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 , where ≥ 4; are periodic in x for 1 ≤ ≤ and 0 is in a gap of the spectrum of -Δ + ; . If for an appropriate constant , we show that this equation has a nontrivial solution.