On a “Zero Mass” Nonlinear Schrödinger Equation-Reference-Cited by-同舟云学术

On a “Zero Mass” Nonlinear Schrödinger Equation

Published:2007-11-01 Issue:4 Volume:7 Page:599-627
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Azzollini Antonio¹,Pomponio Alessio²

Affiliation:

1. Dipartimento di Matematica Universit`a degli Studi di Bari, Via E. Orabona 4, I-70125 Bari, Italy

2. Dipartimento di Matematica Politecnico di Bari, Via Amendola 126/B, I-70126 Bari, Italy

Abstract

Abstract We look for positive solutions to the nonlinear Schrödinger equation −Ɛ2∆u − V (x)f′(u) = 0 in ℝN, where V is a continuous bounded positive potential and f satisfies particular growth conditions which make our problem fall in the so called “zero mass case”. We prove an existence result for any Ɛ > 0, and a multiplicity result for Ɛ sufficiently small.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2007-0406/pdf

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