Structure of Solutions Sets and a Continuous Version of Filippov’s Theorem for First Order Impulsive Differential Inclusions with Periodic Conditions
نویسندگان
چکیده
In this paper, the authors consider the first-order nonresonance impulsive differential inclusion with periodic conditions y′(t)− λy(t) ∈ F (t, y(t)), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(t − k ) = Ik(y(t − k )), k = 1, 2, . . . ,m, y(0) = y(b), where J = [0, b] and F : J × R → P(R) is a set-valued map. The functions Ik characterize the jump of the solutions at impulse points tk (k = 1, 2, . . . ,m). The topological structure of solution sets as well as some of their geometric properties (contractibility and Rδ-sets) are studied. A continuous version of Filippov’s theorem is also proved.
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