Sharp conditions for a class of nonlinear Schrödinger equations

Yang Liu; Jie Liu; Tao Yu; Yang Liu; Jie Liu; Tao Yu

doi:10.3934/mbe.2023174

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3721-3730. doi: 10.3934/mbe.2023174

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Sharp conditions for a class of nonlinear Schrödinger equations

Yang Liu ^{1
,
,},
Jie Liu ²,
Tao Yu ²

1.
College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China
2.
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

Received: 26 October 2022 Revised: 22 November 2022 Accepted: 23 November 2022 Published: 09 December 2022

This paper studies a class of nonlinear Schrödinger equations in two space dimensions. By constructing a variational problem and the so-called invariant manifolds of the evolution flow, we get a sharp condition for global existence and blow-up of solutions.
- nonlinear Schrödinger equations,
- global existence,
- blow-up,
- sharp conditions,
- invariant manifolds
Citation: Yang Liu, Jie Liu, Tao Yu. Sharp conditions for a class of nonlinear Schrödinger equations[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3721-3730. doi: 10.3934/mbe.2023174

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Abstract

This paper studies a class of nonlinear Schrödinger equations in two space dimensions. By constructing a variational problem and the so-called invariant manifolds of the evolution flow, we get a sharp condition for global existence and blow-up of solutions.

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