Exact solutions to some classes of nonlinear integral, integro-functional, and integro-differential equations

Polyanin, A. D. and Zhurov, Alexei I. ORCID: https://orcid.org/0000-0002-5594-0740 2008. Exact solutions to some classes of nonlinear integral, integro-functional, and integro-differential equations. Doklady Mathematics 77 (2) , pp. 315-319. 10.1134/S1064562408020403

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Abstract

The method for constructing exact solutions to certain classes of Urysohn-type nonlinear integral equations is described that generalizes the solution technique for nonlinear equations of the second kind with a degenerate kernel. The method is based on solving a linear auxiliary equation obtained by discarding the nonlinear terms and is extended to nonlinear integro-functional and integro-differential equations. The method described becomes the well-known solution method for second-kind non-linear integral equations with constant limits of integration and a degenerate kernel. The solutions to the original nonlinear integro-functional differential equation are sought in the form where a constant is determined by the algebraic equation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Dentistry
Publisher:	Springer
ISSN:	1064-5624
Last Modified:	18 Oct 2022 13:57
URI:	https://orca.cardiff.ac.uk/id/eprint/16019

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