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Schrödinger equations with asymptotically periodic terms

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  30 June 2015

Reinaldo de Marchi
Reinaldo de Marchi*
Affiliation:
Departamento de Matemática, Universidade Federal de Mato Grosso, Cuiabá 78060-900, Mato Grosso, Brazil (reinaldodemarchi@ufmt.br)
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Abstract

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We study the existence of non-trivial solutions for a class of asymptotically periodic semilinear Schrödinger equations in ℝN. By combining variational methods and the concentration-compactness principle, we obtain a non-trivial solution for the asymptotically periodic case and a ground state solution for the periodic one. In the proofs we apply the mountain pass theorem and its local version.

Keywords

semilinear elliptic equationSchrödinger equationmountain pass theoremasymptotically periodic problemsconcentration-compactness principle

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J61: Semilinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 745 - 757
Copyright
Copyright © Royal Society of Edinburgh 2015