Differential and Integral Equations
- Differential Integral Equations
- Volume 27, Number 7/8 (2014), 671-690.
Nonlinear RLC Circuits and Implicit ODEs
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.
Differential Integral Equations, Volume 27, Number 7/8 (2014), 671-690.
First available in Project Euclid: 6 May 2014
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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