Existence results for -point boundary value problem of second order ordinary differential equations

This study concerns the existence of positive solutions to the boundary value problem u ″ + a ( t ) f ( u ) = 0 , t ∈ ( 0 , 1 ) , u ′ ( 0 ) = ∑ i = 1 n - 2 b i u ′ ( ξ i ) , u ( 1 ) = ∑ i = 1 n - 2 a i u ( ξ i ) , where ξ i ∈ ( 0 , 1 ) with 0 < ξ 1 < ξ 2 < ⋯ < ξ n - 2 < 1 , a i , b i ∈ [ 0 , ∞ ) with 0 < ∑ i = 1 n - 2 a i < 1 and ∑ i = 1 n - 2 b i < 1 . By applying the Krasnoselskiiʹs fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n -point boundary value problem.