Release Time:2019-11-06  Hits:

Indexed by: Journal Papers

Date of Publication: 2019-01-01

Journal: PUBLICATIONES MATHEMATICAE-DEBRECEN

Included Journals: SCIE

Volume: 95

Issue: 1-2

Page Number: 205-217

ISSN: 0033-3883

Key Words: Schrodinger equations; the harmonic oscillator; normal forms

Abstract: We show that the small solution for a type of nonlinear Schrodinger equation with the harmonic potential exists over a longer time interval than the one given by local existence theory. We also get a control of the Sobolev norm of the solution on that time interval. We exploit the structure of nonlinearity to estimate the small divisor and perform a normal form process.