The uniqueness of the periodic solution for a class of differential equations

Abstract

In this paper we are concerned with a class of nonlinear dieren tial equations and obtaining the sucien t conditions for the uniqueness of the periodic solution by using Brouwer's xed point theory and the Sturm Theorem. Keywords. uniqueness, xed point, existence, control theory method, Sturm comparison theorem. AMS (MOS) subject classication: 34C25 where (t; x) 2 (0; 2 ) R and (t; x; z) 2 C 0 ((0; 2 ) R R), f 2 C 2 (0; 2 ) R , and (t; x; x 0 ); f(t; x) are 2 -periodic functions with respect to t.