In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.
We prove an existence and uniqueness theorem for row-finite initial value problems. The right-hand side of the differential equation is supposed to satisfy a one-sided matrix Lipschitz condition with a quasimonotone row-finite matrix which has an at most countable spectrum.
Using interpolation techniques we prove an optimal regularity theorem for the convolution , where is a strongly continuous semigroup in general Banach space. In the case of abstract parabolic problems – that is, when is an analytic semigroup – it lets us recover in a unified way previous regularity results. It may be applied also to some non analytic semigroups, such as the realization of the Ornstein-Uhlenbeck semigroup in , , in which case it yields new optimal regularity results in fractional...
In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions in Hilbert spaces we deal with the existence of periodic oscillations for a class of feedback control systems in Hilbert spaces.
We investigate the existence of solutions on a compact interval to second order boundary value problems for a class of functional differential inclusions in Banach spaces. We rely on a fixed point theorem for condensing maps due to Martelli.