On the existence of solutions connecting singularities in nonlinear RLC circuits. (April 2015)

• Record Type: Journal Article
• Authors: Battelli, Flaviano; Fečkan, Michal
• Is Part Of: Nonlinear analysis. Volume 116(2015)
• Page Start: 26
• Page End: 36
• Publication Date: 2015-04
• Subjects: 34A09 -- 34C23 -- 37G99; Implicit ode -- I-singularity -- Melnikov method; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.015
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We apply dynamical system methods and Melnikov theory to study small amplitude perturbations of some implicit differential equations arising in RLC circuits. We find conditions under which solutions joining two singularities persist after a small forcing. Finally, in the last section we extend this result to a wider class of implicit differential equations.