Qualitative properties of a class differential inclusions

Tzanko Donchev, Sofia, Bulgaria

Keywords: One side Lipschitz multi, differential inclusions AMS Subject classification: 34A60, 34C99, 49J24, 49K24

Abstract: We examine the nonemptiness and some qualitative properties of the solution set of the differential inclusion:

ẍ(t) ∈ F (t, x(t)),  x(0) = x_{0},  t ∈ [0, 1],

where x belongs to a Banach space E and F (t, x) is a compact valued multi. If F (., .) is one side Lipschitz in the state variable, then the solution set is nonempty compact connected, depends continuosly on parameters and is dense in the relaxed solution set.