Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-25T13:36:36.850Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)