Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

Abstract EN

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t)∈F(t,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 ?, I=[0,T], (T>0), F:I×S→?, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x)⊂c(t)x+xp?, ∀(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.