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A comparison method for ordinary differential systems. (English) Zbl 1026.34015

The author establishes sufficient conditions guaranteeing the existence and uniqueness of the solution to a certain system of ordinary differential equations including also delay problems with initial periodic conditions.
It is showed that the method of successive approximations is convergent to this solution under certain assumption. Estimates on errors are given, the problem of uniqueness and continuous dependence is investigated.
The periodic problem for differential systems with delayed arguments is discussed, too. Corresponding results on continuous dependence are also obtained for delayed problems. Related results can be found in T.Jankowski [Zeszyty Nauk. Politech. Gdanskiej, Mat. 16, 3-167 (1993; Zbl 0893.34062)] and V. Lakshmikantham [J. Math. Anal. Appl. 251, 805-817 (2000; Zbl 0966.34055)].

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34B99 Boundary value problems for ordinary differential equations
34K13 Periodic solutions to functional-differential equations
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