On singular solutions of implicit second-order ordinary differential equations

Date

2003-01-01

Author

Bhupal, Mohan Lal

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

208
views

0
downloads

In this note we discuss the notion of singular solutions of completely integrable implicit second-0rder ordinary differential equations. After restricting the class of admissible equations we give conditions under which singular solutions occur in 1-parameter families and as isolated objects. © 2003 by the University of Notre Dame. All rights reserved.

URI

https://hdl.handle.net/11511/69973

Journal

Hokkaido Mathematical Journal

DOI

https://doi.org/10.14492/hokmj/1350659159

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On periodic solutions of differential equations with piecewise constant argument Akhmet, Marat (Elsevier BV, 2008-10-01) The periodic quasilinear system of differential equations with small parameter and piecewise constant argument of generalized type [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA, 66 (2007) 367-383, M.U. Akhmet, On the reduction principle for differential equations with piecewise argument of generalized type, J. Math. Anal. Appl. 336 (2007) 646-663] is addressed. We consider the critical case, when associated linear homogen...
On a transformation between hierarchies of integrable equations GÜRSES, METİN; Zheltukhın, Kostyantyn (Elsevier BV, 2006-02-20) A transformation between a hierarchy of integrable equations arising from the standard R-matrix construction on the algebra of differential operators and a hierarchy of integrable equations arising from a deformation of the standard R-matrix is given.
On the reduction principle for differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-12-01) In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297...
On construction of recursion operators from Lax representation Gurses, M; Karasu, Atalay; Sokolov, VV (1999-12-01) In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations. (C) 1999 American Institute of Physics. [S0022-2488(99)03212-0].
On the Orthogonality of q-Classical Polynomials of the Hahn Class Alvarez-Nodarse, Renato; Adiguzel, Rezan Sevinik; Taşeli, Hasan (2012-01-01) The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric difference equation on a q-linear lattice by means of a qualitative analysis of the q-Pearson equation. To be more specific, a geometrical approach has been used by taking into account every possible rational form of the polynomial coefficients in the q-Pearson equation, together with various relative positions of their zeros, to describe a desired q-wei...

Citation Formats

M. L. Bhupal, “On singular solutions of implicit second-order ordinary differential equations,” Hokkaido Mathematical Journal, pp. 623–641, 2003, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/69973.