Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1168.35437
Zhang, Guoping; Pankov, Alexander
Standing waves of the discrete nonlinear Schrödinger equations with growing potentials. (English)
[J] Commun. Math. Anal. 5, No. 2, 38-49, electronic only (2008). ISSN 1938-9787/e

Summary: We investigate the existence of nontrivial standing wave solution of the discrete nonlinear Schrödinger equation with the growing potential at infinity. Firstly we derive a discrete version of compact embedding theorem. Then combining the Nehari manifold approach and the compact embedding theorem we show the existence of nontrivial standing wave solution without Palais-Smale condition. We also prove the exponential decay of the standing wave solutions.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35Q51 Solitons
47J30 Variational methods

Keywords: discrete nonlinear Schrödinger equation; standing wave; variation methods; Nehari manifold

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]