Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 15, Number 1 (2000), 141-151.
On a controllability problem for systems governed by semilinear functional differential inclusions in Banach spaces
For 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.
Topol. Methods Nonlinear Anal., Volume 15, Number 1 (2000), 141-151.
First available in Project Euclid: 22 August 2016
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Obukhovskiĭ, Valeri; Rubbioni, Paola. On a controllability problem for systems governed by semilinear functional differential inclusions in Banach spaces. Topol. Methods Nonlinear Anal. 15 (2000), no. 1, 141--151. https://projecteuclid.org/euclid.tmna/1471873913