Ovidiu Cârjă

Weak Tangency, Weak Invariance, and Carathéodory Mappings

New results on weak invariance in Hilbert spaces, both in autonomous and nonautonomous case, are given. Applications to weakly decreasing systems and to strong invariance are presented.

On the minimum time function and the minimum energy problem; a nonlinear case☆

Abstract For a semilinear control system in general Banach spaces, we prove results on exact and approximate controllability, regularity of the minimum time function, connections between the minimum time function and the minimum energy.

Nonlocal evolution inclusions under weak conditions

We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the perturbations is weakened to one-sided Lipschitz ones. We prove an existence result for the multipoint problems that cover periodic and antiperiodic cases. We give examples to illustrate the applicability of our results.

Generalized Solutions of Semilinear Evolution Inclusions

In this paper we study different types of (generalized) solutions for semilinear evolution inclusions in general Banach spaces, called limit and weak solutions, which are extensions of the weak solutions studied by T. Donchev [Nonlinear Anal., 16 (1991), pp. 533--542] and the directional solutions studied by J. Tabor [Set-Valued Anal., 14 (2006), pp. 121--148]. Under appropriate assumptions, we show that the set of the limit solutions is compact

How mild can slow controls be

R_\delta

Viability for differential inclusions in Banach spaces

. When the right-hand side satisfies the one-sided Perron condition, a variant of the well-known lemma of Filippov--Plis, as well as a relaxation theorem, are proved.

Lower semicontinuous solutions for a class of Hamilton-Jacobi-Bellman equations

For a linear control system, if a state can be steered to zero in some time, then it can be steered to zero in any larger time and it is expected that, as the time grows, the norm of the corresponding control to be smaller. We study here the behavior of the minimum

Viability, invariance and applications

L^p