Differential and Integral Equations

Nonlinear RLC Circuits and Implicit ODEs

Flaviano Battelli and Michal Fečkan

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 7/8 (2014), 671-690.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1399395748

Mathematical Reviews number (MathSciNet)
MR3200759

Zentralblatt MATH identifier
1340.34044

Subjects
Primary: 34A09: Implicit equations, differential-algebraic equations [See also 65L80] 34C23: Bifurcation [See also 37Gxx] 37G99: None of the above, but in this section

Citation

Battelli, Flaviano; Fečkan, Michal. Nonlinear RLC Circuits and Implicit ODEs. Differential Integral Equations 27 (2014), no. 7/8, 671--690. https://projecteuclid.org/euclid.die/1399395748


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