Constrained differential inclusions with nonlocal initial conditions

Abderrahim Jourani (1) , Emilio Vilches (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 ICEd - UOH - Instituto de Ciencias de la educacion

We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.

Mots clés: Bounding functions; Normal cone; Differential inclusions; Nonlocal Cauchy problem; Periodic solutions; Sweeping processes

Domaines: Optimisation et contrôle [math.OC]

Abderrahim Jourani, Emilio Vilches. Constrained differential inclusions with nonlocal initial conditions. Pure and Applied Functional Analysis, 2018, 3 (3), pp.463-492. ⟨hal-01666584⟩