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Basic results on hybrid differential equations. (English) Zbl 1206.34020
Summary: An existence theorem for hybrid nonlinear differential equations is proved under mixed Lipschitz and Carathéodory conditions. Some fundamental differential inequalities are also established which are utilized to prove the existence of extremal solutions and a comparison result.

##### MSC:
 34A38 Hybrid systems 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions 34A40 Differential inequalities (ODE) 34C10 Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
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##### References:
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