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


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.


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


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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,



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Communications on Pure and Aplied Analysis




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American Institute of Mathematical Sciences

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