Ground state of the mass-critical inhomogeneous nonlinear Schrodinger functional

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Thanh Viet Phan¹ 

[1] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

关键词: Nonlinear Schrodinger equation;    Mass-critical;    Concentration-compactness method;    Bow-up profile;    Gagliardo-Nirenberg inequality;   

DOI  :  10.1016/j.jmaa.2020.123874

来源: Elsevier

【 摘 要 】

We study the ground state problem of the nonlinear Schrodinger functional with a mass-critical inhomogeneous nonlinear term. We provide the optimal condition for the existence of ground states and show that in the critical focusing regime there is a universal blow-up profile given by the unique optimizer of a Gagliardo-Nirenberg interpolation inequality. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free