Abstract
We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed‐point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer′s fixed‐point theorem combined with lower semicontinuous multivalued operators with decomposable values.
Highlights
We are concerned with proving the existence of solutions of differential inclusions, with nonlocal initial conditions
It was remarked that the constants ck, k = 1, . . . , p, from condition (1.1b) can satisfy the inequalities |ck| ≥ 1, k = 1,..., p
As pointed out by Byszewski [4], the study of initial value problems with nonlocal conditions is of significance since they have applications in problems in physics and other areas of applied mathematics
Summary
We are concerned with proving the existence of solutions of differential inclusions, with nonlocal initial conditions. As pointed out by Byszewski [4], the study of initial value problems with nonlocal conditions is of significance since they have applications in problems in physics and other areas of applied mathematics. 426 On a nonlocal Cauchy problem for differential inclusions and Colombo for lower semicontinuous (l.s.c.) multivalued operators with decomposable values, existence results are proposed for problem (1.1). Let E be a Banach space, X a nonempty closed subset of E, and G : X → ᏼ(E) a multivalued operator with nonempty closed values. The multivalued map F is of l.s.c. type if its associated Niemytzki operator Ᏺ is l.s.c. and has nonempty closed and decomposable values. We state a selection theorem due to Bressan and Colombo [3]
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