title: Existence results for differential inclusions with nonlinear growth conditions in Banach spaces.
abstract: In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, x(·)(t) ∈ a.e. on I, x(t) ∈ S, ∀t ∈ I, x(0) = x₀ ∈ S, (∗), where S is a closed subset in a Banach space X, I = [0, T], (T > 0), F : I × S → X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ⊂ c(t)(||x|| + ||x|| (p)K, ∀(t, x) ∈ I × S, where p ∈ ℝ, with p ≠ 1, and c ∈ C([0, T], ℝ(+)). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.
authors.affiliation: Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
authors.forename: Messaoud
authors.initials: M
authors.lastname: Bounkhel
mesh_terms: D055641:Mathematical Concepts; D015233:Models, Statistical; D017711:Nonlinear Dynamics