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Controllability results for nondensely defined evolution differential inclusions with nonlocal conditions. (English) Zbl 1059.34037
The author provides sufficient conditions for the controllability of the following semilinear evolution differential inclusion with nonlocal conditions $$ y'(t)\in Ay(t)+F(t,y(t))+(\Theta u)(t), \quad t\in J=[0,b],\quad y(0)+g(y)=y_{0},$$ where $A:D(A)\subset E\to E$ is a nondensely defined closed linear operator, $F: J\times E\to {\cal P}(E)\backslash\emptyset$ is a multivalued map $({\cal P}$ is the family of all subsets of $E$) and $g:C(J,E)\to E$ is a continuous function. The control function $u(\cdot)$ is given in $L^{2}(J,U)$, a Banach space of admissible control functions with $U$ as a Banach space. Finally, $\Theta$ is a bounded linear operator from $U$ to $E$ and $E$ is a separable Banach space. The proofs rely on the theory of integrated semigroups and the Bohnenblust-Karlin fixed-point theorem.

34G25Evolution inclusions
34H05ODE in connection with control problems
Full Text: DOI
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