On the existence of solutions to some nonlinear integrodifferential equations with delays

I. K. Purnaras, University of Ioannina, Ioannina, Greece

E. J. Qualitative Theory of Diff. Equ., No. 22. (2007), pp. 1-21.

Abstract: Existence of solutions to some nonlinear integral equations with variable delays are obtained by the use of a fixed point theorem due to Dhage. As applications of the main results, existence results to some initial value problems concerning differential equations of higher order as well as integro-differential equations are derived. The case of Lipschitz-type conditions is also considered. Our results improve and generalize, in several ways, existence results already appeared in the literature.

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