Abstract
It is known that the theory of differential equations with multivalued right-hand sides (sometimes also called contingent equations) is closely related to the optimal control theory. Our aim is to show that the technique of the contingent equations is useful in the theory of continuous and discrete boundary value problems too. In section 1 we start wtih a new topological method which permits to establish the existence of solutions provided a criterion of uniqueness is fulfilled. Section 2 contains a result of A.Plis concerning contingent equations [5]. In section 3 and 4 existence theorems for continuous and discrete boundary value problems are given. The main result, an approximation theorem, is stated in section 5.
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