Positive solutions for third-order three-point nonhomogeneous boundary value problems

In this work, by employing the Guo–Krasnosel’skii fixed point theorem and Schauder’s fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary value problem u ‴ ( t ) + a ( t ) f ( u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ′ ( 0 ) = 0 , u ′ ( 1 ) − α u ′ ( η ) = λ , where η ∈ ( 0 , 1 ) , α ∈ [ 0 , 1 / η ) are constants and λ ∈ ( 0 , ∞ ) is a parameter.