Existence and Monotone Method for Periodic Solutions of First Order Differential Equations

Abstract

**Please note that the full text is embargoed** ABSTRACT: An attempt was made recently in [3] to combine fruitfully the two basic techniques, namely the method of upper and lower solutions and the Lyapunov-Schmitt method to investigate the existence of periodic solutions of second order nonlinear boundary value problems. in this paper, we utilize this fruitful approach to study existence of periodic solutions of first order nonlinear differential equations. We also develope monotone iterative technique for obtaining multiple periodic solutions which are obtained as limits of monotone sequences. Since each member of these sequences is a periodic solution of a linear differential equation of first order which can explicitly be computed, the importance of the technique needs no emphasis. Moreover, it is also clear from our proofs that the method of approach is applicable to study other problems at resonance. For other methods of proving existence of periodic solutions see [2,4,5].