Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearities

2014/04/03 by Shaowei Chen, Dawei Zhang, Chen, Shaowei +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1404.0771

arXiv admin note: substantial text overlap with arXiv:1310.2399

arxiv created 2014/04/03 · arxiv updated 2014/04/04

Abstract

We study the Schrödinger equation: - Δu+V(x)u+f(x,u)=0, u∈ H¹(ℝ^N),where V is periodic and f is 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.

Citations

• Existence of nontrivial solutions for asymptotically linear periodic Schrödinger equations

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