NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL-Reference-Cited by-同舟云学术

NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL

Published:2001-11 Issue:04 Volume:03 Page:549-569
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

BARTSCH THOMAS¹,PANKOV ALEXANDER²,WANG ZHI-QIANG³

Affiliation:

1. Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany

2. Department of Mathematics, Vinnitsa State Pedagogical University, 287100 Vinnitsa, Ukraine

3. Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA

Abstract

We investigate nonlinear Schrödinger equations like the model equation [Formula: see text] where the potential Vλ has a potential well with bottom independent of the parameter λ > 0. If λ → ∞ the infimum of the essential spectrum of -Δ + Vλ in L2(ℝN) converges towards ∞ and more and more eigenvalues appear below the essential spectrum. We show that as λ→∞ more and more solutions of the nonlinear Schrödinger equation exist. The solutions lie in H1(ℝN) and are localized near the bottom of the potential well, but not near local minima of the potential. We also investigate the decay rate of the solutions as |x|→∞ as well as their behaviour as λ→∞.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199701000494

Reference19 articles.

1. Quasi topologies and rational approximation

2. Existence and multiplicity results for some superlinear elliptic problems on RN

3. Sign changing solutions of nonlinear Schrödinger equations

4. Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential

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