American Institute of Mathematical Sciences

May  2017, 16(3): 953-972. doi: 10.3934/cpaa.2017046

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

 1 Institut Elie Cartan de Lorraine and CNRS, UMR 7502, Université de Lorraine, Metz, 57045, France 2 Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj, 400084, Romania 3 Department of Mathematics, University of Pécs, Pécs, 7624, Hungary

* Corresponding author

Received  August 2016 Revised  December 2016 Published  February 2017

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.

Citation: Renata Bunoiu, Radu Precup, Csaba Varga. Multiple positive standing wave solutions for schrödinger equations with oscillating state-dependent potentials. Communications on Pure & Applied Analysis, 2017, 16 (3) : 953-972. doi: 10.3934/cpaa.2017046
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