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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 No.: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.