On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\) (Q1754577)
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scientific article; zbMATH DE number 6877120
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\) |
scientific article; zbMATH DE number 6877120 |
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On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\) (English)
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31 May 2018
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This paper deals with a Schrödinger-type equation involving periodic and nonperiodic nonlinearities in the two-dimensional Euclidean space. The problem also contains a potential \(V\) that is 1-periodic and such that 0 lies in a spectral gap of the spectrum of the linear Schrödinger l operator \(-\Delta + V\). The reaction has exponential growth in the sense of Trudinger-Moser. The nonlinear term is allowed to be both periodic and nonperiodic in the spatial variable. The proofs combine the linking theorem and the Lions concentration-compactness principle.
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linear Schrödinger operator
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semilinear equation
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periodic potential
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spectral theory
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