$H^1$-Blow up Solutions for Peker–Choquard Type Schrödinger Equations

2018 ◽  
Author(s):  
Hitoshi Hirata
Keyword(s):  
Blow Up ◽  
Schrodinger Equations ◽  
Schrödinger Equations

Blow-up of solutions to cubic nonlinear Schrödinger equations with defect: The radial case

2017 ◽  
Vol 6 (2) ◽  
pp. 183-197 ◽  
Author(s):  
Olivier Goubet ◽  
Emna Hamraoui
Keyword(s):  
Blow Up ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Radial Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Radial Case ◽  
Nonlinear Schrodinger Equations ◽  
Dimension 2

AbstractIn this article we investigate both numerically and theoretically the influence of a defect on the blow-up of radial solutions to a cubic NLS equation in dimension 2.

scholarly journals A system of Schrödinger equations with general quadratic-type nonlinearities

2020 ◽  
pp. 2050023
Author(s):  
Norman Noguera ◽  
Ademir Pastor
Keyword(s):  
Global Existence ◽  
Variational Methods ◽  
Nonlinear Stability ◽  
Ground State ◽  
Finite Time ◽  
Blow Up ◽  
Quadratic Growth ◽  
Schrodinger Equations ◽  
Concentration Compactness ◽  
Schrödinger Equations

In this work, we study a system of Schrödinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in terms of the ground state solutions associated with the corresponding elliptic system, which in turn are obtained by applying variational methods. By using the concentration-compactness method we also investigate the nonlinear stability/instability of the ground states.

On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth

2021 ◽  
Author(s):  
Amin Esfahani
Keyword(s):  
Blow Up ◽  
Dynamical Behavior ◽  
Critical Growth ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Quadratic Interaction ◽  
Nonlinear Schrodinger Equations ◽  
Normalized Solutions

In this paper, we study the dynamical behavior of solutions of nonlinear Schrödinger equations with quadratic interaction and [Formula: see text]-critical growth. We give sharp conditions under which the existence of global and blow-up solutions are deduced. We also show the existence, stability, and blow-up behavior of normalized solutions of this system.

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