Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent

Martin Schechter, Wenming Zou

Type: Article

Publication Date: 2003-08-01

Citations: 98

DOI: https://doi.org/10.1051/cocv:2003029

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 , where N ≥ 4; V,K,g are periodic in xj for 1 ≤ j ≤ N and 0 is in a gap of the spectrum of -Δ + V; K>0. If for an appropriate constant c, we show that this equation has a nontrivial solution.

Locations

ESAIM Control Optimisation and Calculus of Variations - View - PDF
Springer Link (Chiba Institute of Technology) - View - PDF
French digital mathematics library (Numdam) - View - PDF

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+ PDF Chat	Generalized linking theorem with an application to a semilinear Schrödinger equation	1998	Wojciech Kryszewski Andrzej Szulkin
+	Bifurcation into spectral gaps	1995	C. A. Stuart
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+ PDF Chat	The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1.	1984	Pierre‐Louis Lions
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