In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.
Algorithms for finding an approximate solution of boundary value problems for systems of functional ordinary differential equations are studied. Sufficient conditions for consistency and convergence of these methods are given. In the last section, a construction of methods of arbitrary order is presented.
This paper is concerned with the existence of BV and right continuous solutions for some classes of multivalued differential equations on closed moving sets in Banach spaces.
We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For (bounded variation) data we compare different notions of solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case...