Bounded Solutions of Carathéodory Differential Inclusions: a Bound Sets Approach
نویسندگان
چکیده
We will always consider a Carathéodory set-valued map F : R×RN RN with nonempty, compact, and convex values. We recall that F is said to be a Carathéodory multifunction if F(·,x) is measurable for each x ∈ RN , and F(t,·) is upper semicontinuous for almost all (a.a.) t ∈ R. For the definitions of these standard notions, see, for example, [30]. Our main result is Theorem 4.2. It states the existence of a bounded solution for (1.1). The technique employed in its proof is essentially split into two parts. First, in Section 3 (see Theorem 3.2), given an arbitrary real interval [a,b], we solve the Floquet boundary value problem
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