V. Marinakis
26500, Patras, Hellas
Center of Research and Applications of Nonlinear Systems Department of Mathematics, University of Patras
Publications:
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Marinakis V., Bountis A., Abenda S.
Finitely and Infinitely Sheeted Solutions in Some Classes of Nonlinear ODEs
1998, vol. 3, no. 4, pp. 63-73
Abstract
In this paper we examine an integrable and a non-integrable class of the first order nonlinear ordinary differential equations of the type $\dot{x}=x - x^n + \varepsilon g(t)$, $x \in \mathbb{C}$, $n \in \mathbb{N}$. We exploit, using the analysis proposed in [1], the asymptotic formulas which give the location of the singularities in the complex plane and show that there is an essential difference regarding the formation and the density of the singularities between the cases $g(t)=1$ and $g(t)=t$. Our analytical results are combined with a numerical study of the solutions in the complex time plane.
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