Construction of exact parametric or closed form solutions of some unsolvable classes of nonlinear ODEs (Abel's Nonlinear ODEs of the first kind and relative degenerate equations)

Panayotounakos, DE; Zarmpoutis, TI

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Zarmpoutis, TI	en
dc.date.accessioned	2014-03-01T02:01:55Z
dc.date.available	2014-03-01T02:01:55Z
dc.date.issued	2011	en
dc.identifier.issn	01611712	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29265
dc.title	Construction of exact parametric or closed form solutions of some unsolvable classes of nonlinear ODEs (Abel's Nonlinear ODEs of the first kind and relative degenerate equations)	en
heal.type	journalArticle	en
heal.identifier.primary	10.1155/2011/387429	en
heal.identifier.secondary	http://dx.doi.org/10.1155/2011/387429	en
heal.identifier.secondary	387429	en
heal.publicationDate	2011	en
heal.abstract	We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs) of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions), as well as of the free member of the considered ODE; the parameter being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. The nonlinear initial or boundary value problems are also investigated. Finally, introducing a relative mathematical methodology, we construct the exact parametric or closed form solutions for several degenerate Abel's equation of the first kind. Copyright © 2011 Dimitrios E. Panayotounakos and Theodoros I. Zarmpoutis.	en
heal.journalName	International Journal of Mathematics and Mathematical Sciences	en
dc.identifier.doi	10.1155/2011/387429	en
dc.identifier.volume	2011	en