Closing the gap in the purely elliptic generalized Davey-Stewartson system

A. Eden; H. A. Erbay; G. M. Muslu

doi:10.1016/j.na.2007.08.034

Closing the gap in the purely elliptic generalized Davey-Stewartson system

A. Eden
, H. A. Erbay^*
, G. M. Muslu

^*Corresponding author for this work

Department of Mathematics Engineering

Bogazici University
Scientific and Technological Research Council of Turkey
Isik University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.

Original language	English
Pages (from-to)	2575-2581
Number of pages	7
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	69
Issue number	8
DOIs	https://doi.org/10.1016/j.na.2007.08.034
Publication status	Published - 15 Oct 2008

Funding

The work of the first author is supported by Bogazici University Research Fund.

Funders
Bogazici University Research Fund

Keywords

Blow-up
Davey-Stewartson system
Global existence
Nonlinear Schrödinger equation

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10.1016/j.na.2007.08.034

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abstract = "In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.",

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AU - Eden, A.

AU - Erbay, H. A.

AU - Muslu, G. M.

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Y1 - 2008/10/15

N2 - In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.

AB - In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.

KW - Blow-up

KW - Davey-Stewartson system

KW - Global existence

KW - Nonlinear Schrödinger equation

UR - https://www.scopus.com/pages/publications/50349091573

U2 - 10.1016/j.na.2007.08.034

DO - 10.1016/j.na.2007.08.034

M3 - Article

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JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 8

ER -

Closing the gap in the purely elliptic generalized Davey-Stewartson system

Abstract

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Keywords

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