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, ....

and Applied Analysis 3 The results of this paper can easily to be generalized to the boundary value problems of fractional differential inclusions 1.4 with the following integral boundary conditions: a1x 0 b1 cDγx 0 ) c1 ∫T

A model of stock market dynamics is analyzed using a new approach to uncertainty treatment. The problem of uncertainty is formulated in deterministic way, using the differential inclusions as the main modeling tool. This results in the shape of the reachable set for the model trajectory, namely the possible extreme values of the stock demand and price. The results of example analysis are shown,...

Stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not ne...

This paper is a contribution to the development of a theory concerning stability of equilibrium positions with respect to Sentis solutions of ordinary differential equations with discontinuous right hand side.

In this paper, the existence of solutions and extremal solutions for a perturbed hyperbolic differential inclusion is proved under the mixed generalized Lipschitz and Carathéodory’s conditions.

This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction...

The asymptotic behavior of the solution of a differential inclusion provides a simple proof of a minmax theorem.

Differential inclusions represent an important generalization of differential equations. The solution to a DI is a reachable set, instead of a single trajectory. These concepts are well known in control theory, but not yet exploited in the field of modeling and simulation. The main applications may be related to the uncertainty in dynamic systems. The solving procedure for differential inclusio...