Paola Rubbioni

Nonsmooth feedback controls of nonlocal dispersal models

The paper deals with a nonlocal diffusion equation which is a model for biological invasion and disease spread. A nonsmooth feedback control term is included and the existence of controlled dynamics is proved, satisfying different kinds of nonlocal condition. Jump discontinuities appear in the process. The existence of optimal control strategies is also shown, under suitably regular control functionals. The investigation makes use of techniques of multivalued analysis and is based on the degree theory for condensing operators in Hilbert spaces.

Local mild solutions and impulsive mild solutions for semilinear Cauchy problems involving lower Scorza-Dragoni multifunctions

In this note we investigate in Banach spaces the existence of mild solutions for initial problems, also in presence of impulses, governed by semilinear differential inclusions where the non-linear part is a Scorza-Dragoni multifunction. All the results are obtained via a generalization of {\it Artstein-Prikry selection theorem} that we obtain in the first part of the paper.

Some results on the method of lower and upper solutions for non-compact domains

of the best-known existence results on method lower and upper solutions in initial value problems for systems of O.D.E. is the classical Miiller theorem [l]. According to this fundamental result, for every pair (u, v) of lower and upper solutions, such that u(t) 5 v(t) in [a, b]

Two abstract approaches in vectorial fixed point theory

Abstract In this paper a fixed point theory is established for operators defined on Cartesian product spaces. Two abstract approaches are presented in terms of closure operators and of general functionals called measures of deviations from zero resembling the measures of noncompactness. In particular, we give vectorial versions to Mönch’s fixed point theorems. An application is included to illustrate the theory.

Nonlocal semilinear integro-differential inclusions via vectorial measures of noncompactness

In this note, we show the existence of mild solutions to a nonlocal semilinear integro-differential problem via a new -valued measure of noncompactness involving a Volterra integral operator. Our existence result extends in a broad sense some recent theorems for integro-differential equations. Then we provide a compactness result on the mild solution set and an application to a reaction–diffusion problem involving a distributed time delay.

Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions

In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that the mild solution set is a compact absolute retract (and then a continuum and Rδ-set). As a particular case, the topological structure of the periodic mild solution set is deduced. An illustrating example is supplied.