Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

Abstract

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.

Controllability of integrodifferential equations with state-dependent Delay

“…Theorem 7 [16]. Let A be the infinitesimal generator of a C 0 -semigroup (T(ω)) ω≥0 and let (Λ(ω)) ω≥0 satisfy hypothesis (H2).…”

Existence of solutions for semilinear fractional integro-differential equations with nonlocal conditions

“…In the few past years, some authors have been devoted to research the existence and regularity, periodicity and controllability of solutions for (integro) differential evolution equations with nonlocal conditions. Among others, we refer to Balachandran and Trujillo [3], Brindle and N'Guérékata [7], Chang and Liu [10], Ding et al [14], Ezzinbi et al [19], Ntouyas and Tsamatos [30], Pinaud and Henríquez [31], Vrabie [38], Wang et al [40], Zhang et al [44] and Zhu and Fu [45].…”