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In this paper, the authors consider the first-order nonresonance impulsive differential inclusion with periodic conditions y 0 (t) y(t) 2 F(t,y(t)), a.e. t 2 J\{t1,...,tm}, y(t + ) y(t k ) = Ik(y(t k )), k = 1,2,... ,m, y(0) = y(b), where J = [0,b] and F : J × R n ! P(R n ) 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 R-sets) are studied. A continuous version of Filippov’s theorem is also proved.

Structure of solutions sets and a continuous version of Filippov's theorem for first order impulsive differential inclusions with periodic conditions