On a decay property of solutions to the Haraux-Weissler equation

Reika Fukuizumi; Tohru Ozawa

doi:10.1016/j.jde.2005.02.014

On a decay property of solutions to the Haraux-Weissler equation

Reika Fukuizumi^*, Tohru Ozawa

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We give a sufficient condition that non-radial H¹-solutions to the Haraux-Weissler equation should belong to the weighted Sobolev space H_ρ¹(ℝⁿ), where ρ is the weight function exp ( x ²/4). Our result provides, in some sense, a connection between the solutions obtained by ODE method and those by variational approach in the space H_ρ¹(ℝⁿ).

Original language	English
Pages (from-to)	134-142
Number of pages	9
Journal	Journal of Differential Equations
Volume	221
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2005.02.014
Publication status	Published - 2006 Feb 1
Externally published	Yes

Keywords

Decay estimates
Haraux-Weissler equation
Weighted estimates

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2005.02.014

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abstract = "We give a sufficient condition that non-radial H1-solutions to the Haraux-Weissler equation should belong to the weighted Sobolev space Hρ1(ℝn), where ρ is the weight function exp ( x 2/4). Our result provides, in some sense, a connection between the solutions obtained by ODE method and those by variational approach in the space Hρ1(ℝn).",

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author = "Reika Fukuizumi and Tohru Ozawa",

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AU - Ozawa, Tohru

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N2 - We give a sufficient condition that non-radial H1-solutions to the Haraux-Weissler equation should belong to the weighted Sobolev space Hρ1(ℝn), where ρ is the weight function exp ( x 2/4). Our result provides, in some sense, a connection between the solutions obtained by ODE method and those by variational approach in the space Hρ1(ℝn).

AB - We give a sufficient condition that non-radial H1-solutions to the Haraux-Weissler equation should belong to the weighted Sobolev space Hρ1(ℝn), where ρ is the weight function exp ( x 2/4). Our result provides, in some sense, a connection between the solutions obtained by ODE method and those by variational approach in the space Hρ1(ℝn).

KW - Decay estimates

KW - Haraux-Weissler equation

KW - Weighted estimates

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On a decay property of solutions to the Haraux-Weissler equation

Abstract

Keywords

ASJC Scopus subject areas

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