Existence of noncontinuable solutions of a system ofdifferential equations

Miroslav Bartušek

doi:10.3934/proc.2009.2009.54

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2009, Volume 2009: 54-59. Doi: 10.3934/proc.2009.2009.54 open access

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Existence of noncontinuable solutions of a system of differential equations

Miroslav Bartušek^1,

1.
Masaryk University, Department of Mathematics and Statistics, Kotlarska 2, 611 37 Brno

Received: May 31, 2008

Revised: June 30, 2009

Published: August 2009

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Abstract

In the paper a system of differential equations $y_i^' = f_i(t, y_1,..., y_{n-1}) g_i(y_n)$, $i=1,..., n$ is studied. Sufficient (necessary) conditions for the existence of a solution $y$ fulfilling $lim_{t\to \tau_-} y_i(t)= C_i$, $i=1,2,..., n-1$, $lim_{t\to\tau_-}|y_n(t)|=\infty $ are derived where $\tau<\infty $ and $C_i \in \mathbb{R}$ are given.

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Mathematics Subject Classification: Primary: 34C11.

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