Nonlinear Analysis 50 (2002) 885–898 www.elsevier.com/locate/na Monotone method for rst- and second-order periodic boundary value problems and periodic solutions of functional dierential equations  Daqing Jiang ∗ , Junjie Wei Department of Mathematics, Northeast Normal University, Changchun 130024, People’s Republic of China Received 22 May 2000; accepted 4 December 2000 Keywords: Periodic boundary value problem; Periodic solution; Existence; Upper and lower solution; Monotone iterative technique 1. Introduction The method of upper and lower solutions coupled with the monotone iterative has been applied successfully to obtain results of existence and approximation of solutions for periodic boundary value problems for rst- and second-order ordinary dierential equations (see [1] and references therein). Some attempts have been made to extend these techniques to study periodic bound- ary value problems of functional dierential equations (FDEs). In [2,3], the periodic problem y ′ (t )= f(t;y;y t );y(0) = y(T ) is considered, but in both papers, it is required that f(t;u;) be monotone in the third variable. In this paper, we study rst- and second-order periodic boundary value problems and periodic solutions of functional dierential equations by means of the monotone iterative technique.  The work was supported by NNSF of China. * Corresponding author. E-mail address: daqingjiang@163.com (D. Jiang). 0362-546X/02/$ - see front matter c  2002 Published by Elsevier Science Ltd. PII:S0362-546X(01)00782-9