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Discontinuous first-order functional boundary value problems. (English) Zbl 1210.34088

Summary: We prove a new existence result for functional boundary value problems with first-order functional differential equations under weak conditions on the nonlinear part and monotonicity (but not continuity) with respect to the functional variable. Discontinuities with respect to the unknown are allowed to occur over general classes of time-dependent sets which are assumed to satisfy a kind of unviability or solubility condition.

MSC:

34K10 Boundary value problems for functional-differential equations
34A36 Discontinuous ordinary differential equations
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