On the existence of positive solutions for three-point boundary value problems with alternating coefficients

In this paper, by using the Krasnosel’skii fixed point theorem, we study the existence of at least one or two positive solutions of the three point boundary value problem, { y ″ ( x ) + h ( x ) f ( y ( x ) ) = 0 , x ∈ [ a , b ] α y ( a ) − β y ′ ( a ) = 0 , y ( b ) − δ y ( η ) = 0 , where α ≥ 0 , β ≥ 0 , α + β > 0 , 0 < δ < 1 , η ∈ ( a , b ) and h ( x ) is the alternating coefficient on [ a , b ] . As an application, we also give some examples to demonstrate our results.