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1995 Large time behaviour of solutions of a generalized Haraux-Weissler equation
Claus Dohmen
Differential Integral Equations 8(8): 2065-2078 (1995).

Abstract

We characterize the possible large time behaviors of solutions to $$ (|U|^{m-1} U)'' + {{N-1}\over\eta } (|U|^{m-1} U)' + \beta\eta U' + \alpha U + \gamma |U|^{p-1} U \, =\, 0 \quad \text{ in }\ \mathbb{R}^+ $$ with $m>0$, $p>1$, $\alpha, \beta >0$, $\alpha (m-1)+2\beta >0$ and $\gamma \in \{ -1,0,1\}$. It turns out that if $U$ is bounded and non-constant, $L:= \lim_{\eta\rightarrow\infty } \eta^{\alpha /\beta } U(\eta )$ is always finite and that in the case in which $L=0$, the solutions have compact support ($m>1$), decay exponentially ($m=1$) or decay like $\eta ^{-{2\over{1-m}}}$ ($m<1$), respectively. We want to stress that we impose no sign restriction on the solution.

Citation

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Claus Dohmen. "Large time behaviour of solutions of a generalized Haraux-Weissler equation." Differential Integral Equations 8 (8) 2065 - 2078, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0839.35069
MathSciNet: MR1348965

Subjects:
Primary: 35Q99
Secondary: 34C99, 35B40, 35K99

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 8 • 1995
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