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1. Existence of periodic and positive solutions of nonlinear integro-differential equations with variable delay.

Author

Mesmouli, M. B., Ardjouni, A., and Djoudi, A.

Subjects
*NONLINEAR differential equations, *INTEGRO-differential equations, *MATHEMATICAL variables, *DELAY differential equations, *FIXED point theory, *MATHEMATICAL mappings
Abstract

In this paper, we study the existence of periodic and positive periodic solutions of the nonlinear neutral integro-differential equation x'(t) = - ∫t-τ(t)t a(t,s)x(s)ds + d/dt Q(t,x(t-τ(t))) + G(t,x(t), x(t-τ(t))). We invert this equation to obtain an integral equation. By using Krasnoselski's fixed point Theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness, an example is included to show the feasibility of our results. The positive solutions are studied. [ABSTRACT FROM AUTHOR]

Published
2015

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