A semilinear differential inclusion is considered, assuming that the linear part ia a nondensely defined Yille-Yosida operator whereas Caratheodory-type multivalued nonlinearity satisfies a regularity condition expressed in term of the Hausdorff measure of noncompactness. The theory of integrated semigroups and the fixed point theory for condensing multimaps are applied to obtain local and global solutions and to prove the continuous dependence of the solutions set on initial data. An application to an optimization problem for a feedback control sysyem is given.
On semilinear differential inclusions in Banach spaces with nondensely defined operators / V. Obukhovskii; P. Zecca. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - STAMPA. - 9:(2011), pp. 85-100. [10.1007/s11784-011-0042-3]
On semilinear differential inclusions in Banach spaces with nondensely defined operators
ZECCA, PIETRO
2011
Abstract
A semilinear differential inclusion is considered, assuming that the linear part ia a nondensely defined Yille-Yosida operator whereas Caratheodory-type multivalued nonlinearity satisfies a regularity condition expressed in term of the Hausdorff measure of noncompactness. The theory of integrated semigroups and the fixed point theory for condensing multimaps are applied to obtain local and global solutions and to prove the continuous dependence of the solutions set on initial data. An application to an optimization problem for a feedback control sysyem is given.File | Dimensione | Formato | |
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