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
UR - http://www.scopus.com/inward/citedby.url?scp=84902688222&partnerID=8YFLogxK
U2 - 10.1016/j.na.2014.05.019
DO - 10.1016/j.na.2014.05.019
M3 - Article
AN - SCOPUS:84902688222
SN - 0362-546X
VL - 108
SP - 189
EP - 213
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -