Weak linking theorems and Schrödinger equations with critical Sobolev exponent
ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 601-619.

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 -Δu+V(x)u=K(x)|u| 2 * -2 u+g(x,u),uW 1,2 (𝐑 N ), where N4;V,K,g are periodic in x j for 1jN and 0 is in a gap of the spectrum of -Δ+V; K>0. If 0<g(x,u)uc|u| 2 * for an appropriate constant c, we show that this equation has a nontrivial solution.

DOI: 10.1051/cocv:2003029
Classification: 35B33,  35J65,  35Q55
Keywords: linking, Schrödinger equations, critical Sobolev exponent
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     author = {Schechter, Martin and Zou, Wenming},
     title = {Weak linking theorems and {Schr\"odinger} equations with critical {Sobolev} exponent},
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     url = {http://www.numdam.org/articles/10.1051/cocv:2003029/}
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Schechter, Martin; Zou, Wenming. Weak linking theorems and Schrödinger equations with critical Sobolev exponent. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 601-619. doi : 10.1051/cocv:2003029. http://www.numdam.org/articles/10.1051/cocv:2003029/

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