A Note on the Existence of Periodic Solutions of Second Order Non-Linear Differential Equations

Bahman Mehri, using Leray – Schauder fixed point continuation method, established the existence of periodic solutions to equations of the form,x// +( k+h(x)) x/ + f(t, x) = p(t),where h is a continuous function, f, p are continuous functions in their respective arguments and periodic with respect to t of period ω and k is a constant.The aim of this research is to extend this result to a wider class of equations of the form, x// +( k+h(x)) x/ + F(t, x, x/) = p(t),where F is continuous in t,x and x/; and periodic with respect to t of period ω and k is a constant, using Leray-Schauder fixed point continuation method.