Existence of triple positive solutions for a third-order three-point boundary value problem

Abstract

In this paper we investigate the existence of triple positive solutions for the nonlinear third-order three-point boundary value problemwhere δ ∈ (0, 1), η ∈ [1/2, 1) are constants. f : [0, 1] × [0, ∞) × R 2 → [0, ∞), q : (0, 1) → [0, ∞) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by using a fixed-point theorem due to Avery and Peterson, we establish results on the existence of triple positive solutions to the boundary value problem.

Solvability for a nonlinear third-order three-point boundary value problem

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Existence and iteration of positive solutions to third order three-point BVP with increasing homeomorphism and positive homomorphism

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Existence of positive solutions of three-point boundary value problem for a third-order dynamic equation on time scales

“…In [1], author considered the adequate conditions existence of positive solutions for a second nonlinear boundary value problems. In [2], author discussed the positive solutions of a three order differential equation with three-point boundary value problems.…”