Existence of Nontrivial Solutions for Periodic Schrödinger Equations with New Nonlinearities

Shaowei Chen and Dawei Zhang

Abstract and Applied Analysis, 2014, vol. 2014, 1-10

Abstract:

We study the Schrödinger equation: , where is -periodic and is -periodic in the -variables; is in a gap of the spectrum of the operator . We prove that, under some new assumptions for , this equation has a nontrivial solution. Our assumptions for the nonlinearity are very weak and greatly different from the known assumptions in the literature.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:539639

DOI: 10.1155/2014/539639

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