×

zbMATH — the first resource for mathematics

Continuous dependence of the solution of a system of differential equations with impulses on the initial condition and a parameter in the presence of beating. (English) Zbl 0651.34003
For systems of ordinary differential equations with impulses, the integral curve of the system may meet infinitely many times one and the same of previously fixed hypersurfaces on which the impulses are realized. This phenomenon is called beating. Sufficient conditions for the continuability of the solution of a system of differential equations with impulses in the presence of beating are found. Sufficient conditions for the continuous dependence of the solution on the initial conditions and a parameter are found without imposing conditions for the absence of beating.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1080/00036818408839511 · Zbl 0596.34016 · doi:10.1080/00036818408839511
[2] FILATOV A. N., Averaging Methods in Differential and Integro-differential Equations (1971) · Zbl 0259.34002
[3] HALANAI A., Qualitative Theory of Impulse Systems (1974)
[4] MIL’MAN V. D., Sib. math. J. 1 pp 64– (1960)
[5] PANDIT S. G., Differential Systems Involving Impulses (1982) · Zbl 0539.34001 · doi:10.1007/BFb0067476
[6] DOI: 10.1016/0022-247X(74)90174-7 · Zbl 0303.34042 · doi:10.1016/0022-247X(74)90174-7
[7] SAMOILENKO A. M., Diff. Uravn. 13 pp 1981– (1977)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.