一类二阶常微分方程的泛界性质

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2018-11-06 DOI:10.4171/pm/2026

M. Abdelli, A. Haraux

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引用次数: 2

摘要

我们考虑标量二阶ODE u + |u| $\alpha$ u + |u| $\beta$ u = 0，其中$\alpha$, $\beta$是两个正数，以及系统在(u, u)中在IR 2上生成的非线性半群S(t)。我们证明了S(t)IR 2对于所有t > 0都是有界的，当0 0时，u(t) 2 + |u(t)| $\beta$ +2 $\le$ C {maxt—2$\alpha$, t—($\alpha$ +1)($\beta$ +2) $\beta$—$\alpha$。}

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The universal bound property for a class of second order ODEs

We consider the scalar second order ODE u + |u | $\alpha$ u + |u| $\beta$ u = 0, where $\alpha$, $\beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is bounded for all t > 0 whenever 0 0, u (t) 2 + |u(t)| $\beta$+2 $\le$ C max{t -- 2 $\alpha$ , t -- ($\alpha$+1)($\beta$+2) $\beta$--$\alpha$ }.

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.