Existence of Nontrivial Solutions for Periodic Schrödinger Equations with New Nonlinearities

Shaowei Chen and Dawei Zhang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We study the Schrödinger equation: -Δu+Vxu+fx,u=0, u∈H1(RN), where V is 1‐periodic and f is 1‐periodic in the x‐variables; 0 is in a gap of the spectrum of the operator −Δ + V. We prove that, under some new assumptions for f, this equation has a nontrivial solution. Our assumptions for the nonlinearity f are very weak and greatly different from the known assumptions in the literature.

Date: 2014
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https://doi.org/10.1155/2014/539639

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:539639

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