Applying two three critical points theorems, we prove the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion with a perturbed nonlinearity and two parameters.

The Byrnes-Martin integral invariance principle for ordinary diierential equations is extended to diierential inclusions on R N. The extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes.

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular, quasitriangular structure on group algebra is defined by the pairs of normal inclusions of an finite abelian group and by invariant bimultiplicative form on it. The ...

To motivate a study of asymptotic behaviour of nonlinear systems modelled by ordinary differential equations and differential inclusions, we indicate how such equations/inclusions arise naturally in control of dynamical process by feedback. The concept of control pertains to modifying the behaviour of the process, by manipulation of inputs to the process, in order to achieve some prescribed goa...

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose ‘lifts’ to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize p...

In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of non-compactness we prove two existence theorems. The rst for problems with convex valued orientor elds and the second for problems with nonconvex valued ones.

This paper serves as a corrigendum to the paper titled Application of Pettis integration to delay second order differential inclusions appearing in EJQTDE no. 88, 2012. We present here a corrected version of Theorem 3.1, because Proposition 2.2 is not true. 1 Correction In the above article, Proposition 2.2 is not true since the normed space P 1 E ([0, 1]) is not complete. Consequently, to corr...

Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to ...

We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Som...