Fiinete,Simple and Undirected Graph Encoding
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Date
2014-03
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Addis Ababa University
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 _rst step is to transform the original equation into integrodi
erential equation through a linear integral operator and the second step
is an application of the Schauder's Fixed Point Theorem.
Keywords: Periodic solution; Schauder's _xed point theorem; Fundamental
matrix
Description
Keywords
Periodic solution, Schauder's _xed point theorem, Fundamental matrix