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Advanced Nonlinear Studies

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Volume 16, Issue 2

Issues

Ground States for a Nonlinear Schrödinger System with Sublinear Coupling Terms

Filipe Oliveira / Hugo Tavares
  • Corresponding author
  • CAMGSD & Mathematics Department, IST, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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Published Online: 2016-03-19 | DOI: https://doi.org/10.1515/ans-2015-5029

Abstract

We study the existence of ground states for the coupled Schrödinger system

{-Δui+λiui=μi|ui|2q-2ui+jibij|uj|q|ui|q-2ui,uiH1(n),i=1,,d,

n1, for λi,μi>0, bij=bji>0 (the so-called “symmetric attractive case”) and 1<q<n/(n-2)+. We prove the existence of a nonnegative ground state (u1*,,ud*) with ui* radially decreasing. Moreover, we show that if in addition q<2, such ground states are positive in all dimensions and for all values of the parameters.

Keywords: Nontrivial Ground States; Coupled Nonlinear Schrödinger Systems; Nehari Manifold

MSC 2010: 35J20; 35J50; 35J60

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About the article

Received: 2015-04-15

Accepted: 2015-10-14

Published Online: 2016-03-19

Published in Print: 2016-05-01


Funding Source: Fundação para a Ciência e a Tecnologia

Award identifier / Grant number: UID/MAT/00297/2013

Award identifier / Grant number: Investigador FCT

Award identifier / Grant number: PEst-OE/EEI/LA0009/2013

The first author was partially supported by Fundação para a Ciência e Tecnologia, through contract UID/MAT/00297/2013. The second author was partially supported by Fundação para a Ciência e Tecnologia through the program Investigador FCT and the project PEst-OE/EEI/LA0009/2013, as well as by the ERC Advanced Grant 2013 no. 339958 “Complex Patterns for Strongly Interacting Dynamical Systems – COMPAT”.


Citation Information: Advanced Nonlinear Studies, Volume 16, Issue 2, Pages 381–387, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2015-5029.

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