Vladimirov, A. A.; Krasnosel’skij, M. A.; Chernorutskij, V. V. The Cauchy problem for systems with hysteresis. (English. Russian original) Zbl 0823.34003 Russ. Acad. Sci., Dokl., Math. 48, No. 3, 502-506 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 3, 285-287 (1993). Summary: Systems of ordinary differential equations with hysteresis nonlinearities are studied. General conditions are presented for solvability and uniqueness in the case of the Cauchy problem; the structure of the integral funnel is studied. MSC: 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems, general theory Keywords:systems of ordinary differential equations with hysteresis nonlinearities; uniqueness; Cauchy problem; integral funnel PDF BibTeX XML Cite \textit{A. A. Vladimirov} et al., Russ. Acad. Sci., Dokl., Math. 48, No. 3, 1 (1993; Zbl 0823.34003); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 333, No. 3, 285--287 (1993)