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In this paper, we study existence of solutions of first order dynamic inclusions on time scales with general boundary conditions. Both the ∇-derivative and ∆-derivative cases are considered. Examples are presented to illustrate that the ∆-derivative case needs more restrictive assumptions.  2004 Elsevier Inc. All rights reserved.

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We use subfunctions and superfunctions to derive sufficient conditions for the existence of extremal solutions to initial value problems for ordinary differential equations with discontinuous and singular nonlinearities.