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A first-order semilinear fuzzy differential inclusion with fuzzy impulse characteristics and linear boundary conditions is considered in separable Banach spaces. By means of semigroup properties, stacking approach and the fixed point theorem for multivalued map due to Dhage, the existence results for fuzzy solution are established. Some general criteria are presented for a class of semilinear fuzzy differential inclusions including higher dimensional and infinite dimensional uncertain systems, and the conditions for existence of solutions in the results are concise and mild. Also, several examples are given to illustrate the utility and applicability. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz–Nadler, Bohnenblust–Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems. [Copyright &y& Elsevier]

Abstract: A second order semilinear differential inclusion with some boundary continuous and impulse characteristics in a separable Banach space is considered. Some existence theorems for mild solutions are given, when the multivalued nonlinearity of the inclusion is only a locally integrably bounded upper-Carathéodory map with convex and weakly compact values. Then the compactness of the set of all mild solutions for the problem is proved. The results are obtained by using the theory of continuous cosine families of bounded linear operators and a fixed point theorem for multivalued maps due to Agarwal, Meehan and O’Regan. A corresponding result for closed graph of composition is extended. [Copyright &y& Elsevier]