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 $-\Delta u+V\left(x\right)u={K\left(x\right)|u|}^{{2}^{*}-2}u+g\left(x,u\right),u\in {W}^{1,2}\left({𝐑}^{N}\right)$, where $N\ge 4;V,K,g$ are periodic in ${x}_{j}$ for $1\le j\le N$ and 0 is in a gap of the spectrum of $-\Delta +V$; $K>0$. If $0 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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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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