Sufficient conditions are given for the existence of multiple positive solutions of a boundary value problem of the form x (t)+q(t)f (x(t)) = 0, t ∈ [0, 1], x(0) = 0 and x(1) = R β α x(s)dg(s), where 0 < α < β < 1. A weaker boundary value problem is used to get information on the corresponding integral operator. Then the results follow by applying the Krasnosel'skiȋ fixed point theorem on a suitable cone. 2000 Mathematics Subject Classification. 34B18.

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