In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.2000 Mathematics Subject Classification. 34B15, 34B18.

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problemαη 2 −2η+2T are given constants. We establish the existence of at least three positive solutions by using the Leggett-Williams fixed-point theorem.2000 Mathematics Subject Classification. 34B15, 34C25, 34B18.

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The proof of a result of J. J. Nieto [3] appeared in "Acta Math, Hung."(1992) concerning the positive solutions of nonlinear problems at resonance is corrected and improved.