Order Impulsive Differential Inclusions Research Articles

Existence results for impulsive differential inclusions with nonlocal conditions

In this paper, we investigate the existence of mild solutions for first order impulsive differential inclusions with nonlocal condition in Banach spaces. Our result is obtained using another nonlinear alternative of Leray-Schauder type. An example is also presented.

Neumann boundary value problems for impulsive differential inclusions

In this paper, we investigate the existence of solutions for a class of second order impulsive differential inclusions with Neumann boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values.

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

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.

First order impulsive differential inclusions with periodic conditions

In this paper, we present an impulsive version of Filippov’s Theorem for the first-order nonresonance impulsive differential inclusion 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,...,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,...,m.). Then the relaxed problem is considered and a Filippov-Wasewski result is obtained. We also consider periodic solutions of the first order impulsive differential inclusion y 0 (t) 2 '(t,y(t)), a.e. t 2 J\{t1,...,tm}, y(t + ) y(t k ) = Ik(y(t k )), k = 1,... ,m, y(0) = y(b), where ' : J ×R n ! P(R n ) is a multi-valued map. The study of the above prob[

On initial value problems for a class of first order impulsive differential inclusions

On initial value problems for a class of first order impulsive differential inclusions