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We prove several new existence results for a nonlinear anti-periodic first order problem using a Leray-Schauder alternative. Two definitions of lower and upper solutions are presented and we show in this paper the validity of the lower and upper solution method. Also, we give a method to generate a sequence of approximate solutions converging to a solution of the anti-periodic problem. ∗First and second authors were supported in part by D.G.E.S.I.C. (Spain), project PB97 – 0552. †This is the preprint version of the paper published in Journal of Mathematical Inequalities and Applications, Vol. 6 (2003) 477–485. ‡Corresponding author

Anti-periodic boundary value problem for nonlinear first order ordinary differential equations