Existence theory for functional initial value problems of ordinary differential equations

B. C. Dhage, Kasubai, Gurucul Colony, Maharashtra, India

E. J. Qualitative Theory of Diff. Equ., No. 15. (2004), pp. 1-14.

Abstract: In this paper the existence of a solution of general nonlinear functional differential equations is proved under mixed generalized Lipschitz and Carath\'eodory condition. An existence theorem for the extremal solutions is also proved under certain monotonicity and weaker continuity conditions. Examples are provided to illustrate the abstract theory developed in this paper.

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