Geodesic
Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 35 (2015) no. 1, pp. 25-46.

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This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.
Keywords: controllability, integrodifferential equations, nonlocal initial condition, resolvent operator, Mönch fixed-point theorem 
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Ezzinbi, Khalil; Degla, Guy; Ndambomve, Patrice. Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 35 (2015) no. 1, pp. 25-46. http://geodesic.mathdoc.fr/item/DMDICO_2015_35_1_a1/

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