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

Keywords: Positive solutions Third-order three-point BVPs Nonhomogeneous Fixed point theorem Existence and nonexistence a b s t r a c t 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) − αu (η) = λ, where η ∈ (0, 1), α ∈ [0, 1/η) are constants and λ ∈ (0, ∞) is a parameter.