GLOBAL EXISTENCE AND BLOW-UP FOR THE FOCUSING INHOMOGENEOUS NONLINEAR SCHRODINGER EQUATION WITH INVERSE-SQUARE POTENTIAL

被引：3
作者：
An, Jinmyong [1 ]
Jang, Roesong [1 ]
Kim, Jinmyong [1 ]
机构：
[1] Kim Il Sung Univ, Fac Math, Pyongyang, North Korea
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2023年 / 28卷 / 02期
关键词：
Inhomogeneous nonlinear Schrodinger equation; inverse-square potential; global existence; blow-up; ground state; ENERGY-CRITICAL NLS; SCATTERING;
D O I：
10.3934/dcdsb.2022111
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schrodinger equation with inverse-square potential iu(t) + Delta u - c|x|(-2)u + |x|(-b)|u|(sigma) u = 0; u(0) = u(0) is an element of H-c(1), (t, x) is an element of R x R-d, where d >= 3, 0 < b < 2, 4-2b/d < sigma < 4-2b/d-2 and c > -c(d) := -(d-2/2)(2). We first establish the criteria for global existence and blow-up of general (not necessarily radial or finite variance) solutions to the equation. Using these criteria, we study the global existence and blow-up of solutions to the equation with general data lying below, at, and above the ground state threshold. Our results extend the global existence and blow-up results of Campos-Guzman (Z. Angew. Math. Phys., 2021) and Dinh-Keraani (SIAM J. Math. Anal., 2021).
引用
收藏
页码：1046 / 1067
页数：22
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