The author deals with the three-point boundary value problem
with , is continuous and nonnegative for .
Using properties of the Green function of the corresponding linear problem and a theorem by R. W. Leggett and L. R. Williams [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)], the author proves the existence of at least three positive solutions to (1).