Almost Continuability of Solutions of Differential Equations

S. A. Belyaev

Moscow Institute of Physics and Technology

Abstract: We introduce the notion of almost continuability of the solution of the differential equation of first order $dy/dx=f(x,y)$ to the whole real axis. We give a criterion for the almost continuability of solutions for the case in which the right-hand side of the equation is a meromorphic function of one variable $y$: $f(x,y)=g(y)$. As an example, we work out the case of a rational and, in particular, an entire function $g(y)$.

Keywords: differential equation of first order, almost continuability, pole of a meromorphic function, rational function, Cauchy problem.

UDC: 519.614

Received: 15.06.2007
Revised: 21.04.2008

DOI: 10.4213/mzm4167

 English version: Mathematical Notes, 2009, 85:1, 3–10

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