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July/August 2014 Nonlinear RLC Circuits and Implicit ODEs
Flaviano Battelli, Michal Fečkan
Differential Integral Equations 27(7/8): 671-690 (July/August 2014).

Abstract

We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some implicit differential equations exhibiting I--singularities (in the sense given in [16, p. 166]). In particular, we show persistence of such I-singularities and orbits connecting them in finite time provided a Melnikov like condition holds. We start from a concrete example where, we prove that this Melnikov condition actually holds. Then, we extend our results to more general implicit differential equations.

Citation

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Flaviano Battelli. Michal Fečkan. "Nonlinear RLC Circuits and Implicit ODEs." Differential Integral Equations 27 (7/8) 671 - 690, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1340.34044
MathSciNet: MR3200759

Subjects:
Primary: 34A09, 34C23, 37G99

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 7/8 • July/August 2014
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