Existence of noncontinuable solutions of a system of
differential equations
Miroslav BartuĊĦek - Masaryk University, Department of Mathematics and Statistics, Kotlarska 2, 611 37 Brno, Czech Republic (email) 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.
Keywords: Noncontinuable solutions, singular solutions of the
second kind, system of differential equations
Received: June 2008; Revised: July 2009; Published: September 2009. |