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ON A CLASS OF ELLIPTIC SYSTEM OF SCHRÖDINGER–POISSON TYPE

Part of: Elliptic equations and systems Partial differential equations Representations of solutions

Published online by Cambridge University Press:  24 September 2014

LUCAS C. F. FERREIRA ,
EVERALDO S. MEDEIROS  and
MARCELO MONTENEGRO
LUCAS C. F. FERREIRA
Affiliation:
Universidade Estadual de Campinas, IMECC – Departamento de Matemática, CEP 13083-859, Campinas-SP, Brazil email lcff@ime.unicamp.br
EVERALDO S. MEDEIROS*
Affiliation:
Universidade Federal da Paraíba, Departamento de Matemática, CEP 58051-900, João Pessoa-PB, Brazil email everaldo@mat.ufpb.br
MARCELO MONTENEGRO
Affiliation:
Universidade Estadual de Campinas, IMECC – Departamento de Matemática, CEP 13083-859, Campinas-SP, Brazil email msm@ime.unicamp.br
*
✉everaldo@mat.ufpb.br
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Abstract

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In this paper we prove existence and qualitative properties of solutions for a nonlinear elliptic system arising from the coupling of the nonlinear Schrödinger equation with the Poisson equation. We use a contraction map approach together with estimates of the Bessel potential used to rewrite the system in an integral form.

Keywords

Schrödinger equationsexistencesymmetrypositivityBessel potential

MSC classification

Secondary: 35J61: Semilinear elliptic equations 35J47: Second-order elliptic systems 35C15: Integral representations of solutions 35B06: Symmetries, invariants, etc. 35B09: Positive solutions 35B30: Dependence of solutions on initial and boundary data, parameters

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 97 , Issue 3 , December 2014 , pp. 301 - 314
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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