Existence theory for nonlinear functional boundary value problems

B. C. Dhage, Kasubai, Gurucul Colony, Maharashtra, India
J. Henderson, Baylor University, Waco, Texas, U.S.A.

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

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

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