Dynamics of blow-up solutions for the Schrödinger–Choquard equation

Boundary Value Problems

Kun Liu¹  Cunqin Shi¹ 

[1] School of Mathematics and Statistic, Longdong University;

关键词: Nonlinear Schrödinger–Choquard equation;    Blow-up solutions;    The dynamical properties;   

DOI  :  10.1186/s13661-018-0985-z

来源: DOAJ

【 摘 要 】

Abstract In this paper, we study the dynamics of blow-up solutions for the nonlinear Schrödinger–Choquard equation iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. $$i\psi_{t}+\Delta \psi =\lambda_{1}\vert \psi \vert ^{p_{1}}\psi +\lambda_{2}\bigl(I _{\alpha }\ast \vert \psi \vert ^{p_{2}}\bigr)\vert \psi \vert ^{p_{2}-2}\psi. $$ We first show existence of blow-up solutions and obtain a sharp threshold mass of global existence and blow-up for this equation with λ1>0 $\lambda_{1}>0$, λ2<0 $\lambda_{2}<0$, 0

【 授权许可】

Unknown