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Viability theorems for a class of differential-operator inclusions

Shuzhong, Shi (1989), Viability theorems for a class of differential-operator inclusions, Journal of Differential Equations, 79, 2, p. 232-257. http://dx.doi.org/10.1016/0022-0396(89)90101-0

Type
Article accepté pour publication ou publié
Date
1989
Journal name
Journal of Differential Equations
Volume
79
Number
2
Publisher
Elsevier
Pages
232-257
Publication identifier
Metadata
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Author(s)
Shuzhong, Shi
Abstract (EN)
This paper discusses the following viability problem of a differential inclusion, x′(t) + Ax(t) ϵF(x(t))x(0) = x0ϵK∀t ⩾ 0, x(t) ϵK, where K is a compact subset of a Banach space X, − A is the infinitesimal generator of a compact differentiable semigroup of bounded linear operators on X, and F: K ⇉ X is upper semicontinuous with compact convex values. We show that a natural tanegential condition is necessary and sufficient for the existence of a global solution to this problem.
Subjects / Keywords
viability problem; differential inclusion