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Existence and controllability results for mixed functional integrodifferential equations with infinite delay

Kucche K. D.

Demonstratio Mathematica

2014

Vol. 47, nr 4

893--909

Sufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.

Global existence for abstract nonlinear Volterra-Fredholm functional integrodifferential equation

Dhakne M. B., Kucche K. D.

Demonstratio Mathematica

2012

Vol. 45, nr 1

117-127

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of solution.