TY - JOUR

T1 - Global existence of solutions for a subcritical nonlinear Schrödinger equation

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

N1 - Funding Information:
The work of N.H. is supported by JSPS KAKENHI Grant Numbers 24654034 , and 25220702 . The work of P.I.N. is partially supported by CONACYT Grant Number 166579 and PAPIIT project IN100113 .

PY - 2014/10

Y1 - 2014/10

N2 - We consider the one dimensional nonlinear Schrödinger equation {iut+1/2uxx=N(u,ū),x∈R,t>1,u(1,x)= u0(x),x∈R, where the nonlinearity N(u,ū)=| u|-2γu3=u3-2γū -2γ, the exponent γ>0 is sufficiently small. Our purpose in this paper is to prove a global existence in time of small solutions.

AB - We consider the one dimensional nonlinear Schrödinger equation {iut+1/2uxx=N(u,ū),x∈R,t>1,u(1,x)= u0(x),x∈R, where the nonlinearity N(u,ū)=| u|-2γu3=u3-2γū -2γ, the exponent γ>0 is sufficiently small. Our purpose in this paper is to prove a global existence in time of small solutions.

KW - Global existence

KW - Nonlinear Schrödinger equation

KW - Subcritical case

UR - http://www.scopus.com/inward/record.url?scp=84902688222&partnerID=8YFLogxK

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U2 - 10.1016/j.na.2014.05.019

DO - 10.1016/j.na.2014.05.019

M3 - Article

AN - SCOPUS:84902688222

VL - 108

SP - 189

EP - 213

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -