Abstract: In the present paper we are concerned with the following differential equation with pcriodic coefficients y' = f(t,y) = A(t)y" + B(t)y + C(t) (m>=2,m ∈N) (1)and obtain the theorems for the existence and the number of equation (1). Our results extend and improve the corresponding ones in [1,4]. 

Key words:  differential ,  equation;periodic ,  solution;fixed , point;existence