Valentina Taddei

Nonlocal semilinear evolution equations without strong compactness: theory and applications

A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. No strong compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. A wide family of nonlocal associated boundary value problems is investigated by means of a fixed point technique. Applications are given to an optimal feedback control problem, to a nonlinear hyperbolic integro-differential equation arising in age-structure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.MSC:34G25, 34B10, 34B15, 47H04, 28B20, 34H05.

Floquet Boundary Value Problems for Differential Inclusions: a Bound Sets Approach

A technique is developed for the solvability of the Floquet boundary value problem associated to a differential inclusion. It is based on the usage of a not necessarily C-class of Liapunov-like bounding functions. Certain viability arguments are applied for this aim. Some illustrating examples are supplied.

Bounded solutions of Carathéodory differential inclusions: a bound sets approach

A bound sets technique is developed for Floquet problems of Caratheodory differential inclusions. It relies on the construction of either continuous or locally ipschitzian Lyapunov-like bounding functions. Proceeding sequentially, the existence of bounded trajectories is then obtained. Nontrivial examples are supplied to illustrate our approach.

On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

BVP for Caratheodory inclusions in Hilbert spaces: sharp existence conditions and applications

Abstract This article concerns an existence result for Floquet boundary value problems associated to semilinear differential inclusions with Carathéodory right hand side in a Hilbert space. We apply a continuation principle and we require a sharp (i.e., localized on the boundary) transversality condition. We give an application to a nonlinear partial differential inclusion with periodic conditions.

Bounded solutions and wavefronts for discrete dynamics

This paper deals with the second order nonlinear difference equation

Global exponential stability of the periodic solution of a delayed neural network with discontinuous activations

\dd(r_k\dd u_k)+q_kg(u_{k+1})=0,

Controllability for systems governed by semilinear evolution inclusions without compactness

where