Multiple positive standing wave solutions for Schrödinger equations with oscillating state-dependent potentials

Abstract

Motivated by relevant physical applications, we study Schrödinger equations with state-dependent potentials. Existence, localization and multiplicity results are established for positive standing wave solutions in the case of oscillating potentials. To this aim, a localized Pucci-Serrin type critical point theorem is first obtained. Two examples are then given to illustrate the new theory.

Authors

Renata Bunoiu
Institut Elie Cartan de Lorraine and CNRS, UMR 7502, Univerité de Lorraine, Metz, 57045, France

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Csaba Varga
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj, 400084, Romania
Department of Mathematics, University of Pécs, Pécs, 7624, Hungary

Keywords

Paper coordinates

R. Bunoiu, R. Precup, C. Varga, Multiple positive standing wave solutions for Schrödinger equations with oscillating state-dependent potentials, Comm. Pure Appl. Anal. 16 (2017), 953-972, http://dx.doi.org/10.3934/cpaa.2017046

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About this paper

Journal

Communications on Pure and Aplied Analysis

 

 

 

Publisher Name

American Institute of Mathematical Sciences

Print ISSN
Online ISSN
15340392

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