Geodesic
Almost Continuability of Solutions of Differential Equations
Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {S. A. Belyaev},
     title = {Almost {Continuability} of {Solutions} of {Differential} {Equations}},
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S. A. Belyaev. Almost Continuability of Solutions of Differential Equations. Matematičeskie zametki, Tome 85 (2009) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/MZM_2009_85_1_a0/

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