1998 Generalized linking theorem with an application to a semilinear Schrödinger equation
Wojciech Kryszewski, Andrzej Szulkin
Adv. Differential Equations 3(3): 441-472 (1998). DOI: 10.57262/ade/1366399849

Abstract

Consider the semilinear Schrödinger equation (*) $-\Delta u + V(x)u = f(x,u)$, $u\in H^1(\mathbf {R} ^N)$. It is shown that if $f$, $V$ are periodic in the $x$-variables, $f$ is superlinear at $u=0$ and $\pm\infty$ and 0 lies in a spectral gap of $-\Delta+V$, then (*) has at least one nontrivial solution. If in addition $f$ is odd in $u$, then (*) has infinitely many (geometrically distinct) solutions. The proofs rely on a degree-theory and a linking-type argument developed in this paper.

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Wojciech Kryszewski. Andrzej Szulkin. "Generalized linking theorem with an application to a semilinear Schrödinger equation." Adv. Differential Equations 3 (3) 441 - 472, 1998. https://doi.org/10.57262/ade/1366399849

Information

Published: 1998
First available in Project Euclid: 19 April 2013

MathSciNet: MR1751952
zbMATH: 0947.35061
Digital Object Identifier: 10.57262/ade/1366399849

Subjects:
Primary: 58E05
Secondary: 35J60 , 35Q55 , 47J30

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.3 • No. 3 • 1998
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