New existence and symmetry results for least energy positive solutions of Schrodinger systems with mixed competition and cooperation terms

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Soave, Nicola¹  Tavares, Hugo² 

[1] Univ Giessen, Math Inst, Arndtstr 2, D-35392 Giessen, Germany

[2] Univ Lisbon, Inst Super Tecn, Dept Math, Ctr Math Anal Geometry & Dynam Syst, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

关键词: Competitive and cooperative systems;    Foliated Schwarz symmetry;    Least energy positive solutions;    Nehari manifold;    Positive solutions;    Schrodinger cubic systems;   

DOI  :  10.1016/j.jde.2016.03.015

来源: Elsevier

【 摘 要 】

In this paper we focus on existence and symmetry properties of solutions to the cubic Schrodinger system -Delta u(i) + lambda(i)u(i) = Sigma(d)(j=1)beta(ij)u(j)(2)u(i) in Omega subset of R-N, i = 1, ... d where d >= 2, lambda(i), beta(ii) > 0, beta(ij) = beta(ji) is an element of R for j not equal i, N = 2, 3. The underlying domain Omega is either bounded or the whole space, and u(i) is an element of H-0(1) (Omega) or u(i) is an element of H-rad(1)(R-N) respectively. We establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients, as well as in the purely cooperative case. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free