Sahle, Weldemichael Tesfagiorgis (2014) Existence of Periodic Solutions for a Class of Second Order Odes with Periodic Data. Masters thesis, Addis Ababa University.
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Abstract
In this project we will see the existence of periodic solution(s) to the second order ODE of the form: −x00(t) + a(t)x0(t) = g(t; x) − f(t; x(t); x0(t)) by means of Schauders Fixed Point Theorem where a is a continuous !- periodic function , g(t; u), f(t; u; v) are !-periodic functions in t for u = x(t), v = x0(t) and ! > 0. The method of proof is composed of two steps, the first step is to transform the original equation into integrodifferential equation through a linear integral operator and the second step is an application of the Schauder’s Fixed Point Theorem.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Periodic solution; Schauder’s fixed point theorem; Fundamental matrix. |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Africana |
| Depositing User: | Selom Ghislain |
| Date Deposited: | 24 May 2018 14:35 |
| Last Modified: | 24 May 2018 14:35 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/4103 |
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