Fiinetesimple And Undirected Graph Encoding

In this project we will see the existence of periodic solution(s) to the secondrnorder ODE of the form:rnx00(t) + a(t)x0(t) = g(t; x) f(t; x(t); x0(t))rnby means of Schauders Fixed Point Theorem where a is a continuous !-rnperiodic function , g(t; u), f(t; u; v) are !-periodic functions in t forrnu = x(t), v = x0(t) and ! > 0. The method of proof is composed ofrntwo steps, the _rst step is to transform the original equation into integrodirnerential equation through a linear integral operator and the second steprnis an application of the Schauder's Fixed Point Theorem.rnKeywords: Periodic solution; Schauder's _xed point theorem; Fundamentalrnmatrix

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