On a class of differential equations in Banach space
In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.
We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential of a uniformly regular function V.
We prove several results on lower bounds for the periods of periodic solutions of some classes of functional-differential equations in Hilbert and Banach spaces and difference inclusions 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.