Ava Shafeeq Rafeeq

Conference

2018

5th international Conference on Applied Science, Energy and Environment

2018-04

Consider the following non-linear system of differential equation which has the form: 𝒅𝒙(𝒕)/𝒅𝒕+ 𝒂(𝒕)𝒉(𝒚(𝒕)) = 𝒇(𝒕, 𝒙(𝒕 − 𝝉(𝒕)), 𝒚(𝒕 − 𝝉(𝒕)), 𝒅𝟐𝒚(𝒕)/𝒅𝒕𝟐 + 𝒑(𝒕)𝒅𝒚(𝒕)/𝒅𝒕+ 𝒒(𝒕)𝑱(𝒙(𝒕)) = 𝒈(𝒕, 𝒙(𝒕 − 𝝉(𝒕)), 𝒚(𝒕 − 𝝉(𝒕)) The aim of this paper is to use Krasnoselskii's fixed point theorem to show the existence of a positive periodic solutions for the above system. To apply Krasnoselskii's fixed point theorem requirement to construct two mappings; one is compact and the other is contraction. Using the contraction mapping principle enables us to show the uniqueness of the periodic solution.

2017

2th International Scientific Conference University of Zakho

2017-04

In this paper, we investigate the existence, uniqueness and stability of the periodic solution for the system of nonlinear integro-differential equations by using the numerical-analytic methods for investigate the solutions and the periodic solutions of ordinary differential equations, which are given by A. Samoilenko.