Periodic solutions of some Nonlinear Boundary Value Problems of ODE's

Existence of periodic solutions for higher order ordinary differential equations by the use of Leray- Schauder fixed-point technique depended mainly on the availability of suitable boundedness results. In some cases however, boundedness results were very difficult to establish because of the nature of the Lyapunov functions involved. In this thesis, existence results have been obtained using the Leray- Schauder fixed point technique and the integrated equations for the more general equations of the form : ... x + f (x¨) + a1x? + a2x = p (t) x(4) + g ( ... x) + b1x¨ + b2x? + b3x = p (t) x(5) + c1x(4) + h x, x? , x¨, ... x, x(4) ... x + c2x¨ + c3x? + c4x = p (t) where f = f (¨x) , g = g ( ... x) , h = h