Prescribed mass ground states for a doubly nonlinear Schrodinger equation in dimension one

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Boni, Filippo^1,2  Dovetta, Simone³ 

[1] Politecn Torino, Dipartimento Sci Matemat GL Lagrange, Cso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

[3] Ist Matemat Applicata & Tecnol Informat E Magenes, Via Adolfo Ferrata 1, I-27100 Pavia, Italy

关键词: Nonlinear Schrodinger;    Pointwise nonlinearity;    Fixed mass ground states;    Threshold phenomena;    Minimization;   

DOI  :  10.1016/j.jmaa.2020.124797

来源: Elsevier

【 摘 要 】

We investigate the problem of existence and uniqueness of ground states at fixed mass for two families of focusing nonlinear Schrodinger equations on the line. The first family consists of NLS with power nonlinearities concentrated at a point. For such model, we prove existence and uniqueness of ground states at every mass when the nonlinearity power is L-2-subcritical and at a threshold value of the mass in the L-2-critical regime. The second family is obtained by adding a standard power nonlinearity to the previous setting. In this case, we prove existence and uniqueness at every mass in the doubly subcritical case, namely when both the powers related to the pointwise and the standard nonlinearity are subcritical. If only one power is critical, then existence and uniqueness hold only at masses lower than the critical mass associated to the critical nonlinearity. Finally, in the doubly critical case ground states exist only at critical mass, whose value results from a non-trivial interplay between the two nonlinearities. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free