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Zbl 1059.34037
Gatsori, E.P.
Controllability results for nondensely defined evolution differential inclusions with nonlocal conditions.
(English)
[J] J. Math. Anal. Appl. 297, No. 1, 194-211 (2004). ISSN 0022-247X

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.
[Mouffak Benchohra (Sidi Bel Abbes)]
MSC 2000:
*34G25 Evolution inclusions
34H05 ODE in connection with control problems
93B05 Controllability

Keywords: nondensely defined; controllability; fixed-point; nonlocal conditions

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