Existence and nonexistence of bound state solutions for Schrodinger systems with linear and nonlinear couplings

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Luo, Haijun¹  Zhang, Zhitao^2,3 

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

关键词: Nonlinear Schrodinger equations;    Bound state solution;    Perturbation method;    Pohozaev-Nehari identity;   

DOI  :  10.1016/j.jmaa.2019.02.045

来源: Elsevier

【 摘 要 】

We study the Schrodinger systems with linear and nonlinear coupling terms (doubly coupled nonlinear Schrodinger system for short) which arise naturally in nonlinear optics, and in the Hartree-Fock theory for Bose-Einstein condensates, among other physical problems. First, for small linear coupling constant, we get existence of a nontrivial bound state solution to the system via perturbation method, furthermore, we prove each component of the bound state solution is nonnegative by energy estimate. Second, we establish a version of Pohozaev-Nehari identity and prove a nonexistence result for the more general system when the spatial dimension N >= 4. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free