, Lanzhou 730070, China)This paper deals with the existence of odd periodic solutions for three order ordinary differential equation u′′′t=ft,ut,u′t, where f:R×R2→R is a continuous odd function and ft,u,vis2π periodic in t. Under a condition allowing that ft,u,v is superlinear in u and v, we obtain an existence and uniqueness result. Our discussion is based on the Leray Schauder fixed point theorem.
