Necessary and sufficient conditions for viability for semilinear differential inclusions

Necessary and Sufficient Conditions for Viability for Semilinear Differential Inclusions

Given a set K in a Banach space X, we define: the tangent set, and the quasi-tangent set to K at ξ ∈ K, concepts more general than the one of tangent vector introduced by Bouligand (1930) and Severi (1931). Both notions prove very suitable in the study of viability problems referring to differential inclusions. Namely, we establish several new necessary, and even necessary and sufficient condit...

A Viability Result for Nonconvex Semilinear Functional Differential Inclusions

We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

Necessary conditions of optimality for measure driven differential inclusions

Minimize h(x(0), x(1)) subject to dx(t) ∈ F (t, x(t))dt + G(t, x(t))dμ(t) ∀t∈[0, 1] (x(0), x(1)) ∈ C ⊂ IR × IR l(t, x(t)) ≤ 0 ∀t∈[0, 1] dμ ∈ K where h : IR × IR → IR, and l : [0, 1]× IR → IR are given functions, F : [0, 1]× IR → P(IRn), and G : [0, 1] × IR → P(IRn×q) are given set-valued maps, K ⊂ C∗([0, 1];K) is the set of control measures supported on [0, 1] with range in a given set K ⊂ IR, ...

On controllability for nonconvex semilinear differential inclusions

We consider a semilinear differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.