Periodic solutions of neutral nonlinear system of differential equations with functional delay

By Muhammad N. Islam, Youssef N. Raffoul. 2007

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Abstract We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form d d t x ( t ) = A ( t ) x ( t ) + d d t Q ( t , x ( t − g ( t ) ) ) + G ( t , x ( t ) , x ( t − g ( t ) ) ) . In the process we use the fundamental matrix solution of y ′ = A ( t ) y and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution of the equation.

Subfields: Applied Mathematics, Numerical Analysis

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