On a controllability problem for systems governed by semilinear functional differential inclusions in Banach spaces
KeywordsControllability, functional differential inclusion, condensing multimap, fixed point
AbstractFor a Banach space $E$, a given pair $(\overline p, \overline x)\in[0,a]\times E$, and control system governed by a semilinear functional differential includion of the form $$ x' (t)\in Ax(t) +F(t, x(t), Tx) $$ the existence of a mild trajectory of $x(t)$ satisfying the condition $x(\overline p)=\overline x$ is considered. Using topological methods we develop an unified approach to the cases when a multivalued nonlinearity $F$ is Carathéodory upper semicontinuous or almost lower semicontinuous and an abstract extension operator $T$ allows to deal with variable and infinite delay. For the Carathéodory case, the compactness of the solutions set and, as a corollary, an optimization result are obtained.
How to Cite
OBUKHOVSKIĬ, Valeri & RUBBIONI, Paola. On a controllability problem for systems governed by semilinear functional differential inclusions in Banach spaces. Topological Methods in Nonlinear Analysis [online]. 1 March 2000, T. 15, nr 1, s. 141–151. [accessed 28.3.2023].
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