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Abstract: In this paper, we prove some existence results for a third order multi-point boundary value problem at resonance. Our method is based upon the coincidence degree theory of Mawhin. [Copyright &y& Elsevier]

Abstract: In this paper, we provide sufficient conditions for the existence of at least three solutions to a three-point boundary value problem for higher-order ordinary differential equations. The nonlinear term f in the differential equation under consideration may depend on higher-order derivatives of arbitrary order and this is where the main novelty of this work lies. By applying the two pairs of upper and lower solutions method of Henderson and Thompson, as well as degree theory, the existence of at least three solutions of the problem is given. [Copyright &y& Elsevier]

In this paper, we are concerned with the following third-order ordinary differential equation: with the nonlinear boundary conditions where A,B∈R, f :[0,1]×R3→R is continuous, g,h:R2→R are continuous. The existence result is given by using a priori estimate, Nagumo condition, upper and lower solutions and Leray–Schauder degree, and we give an example to demonstrate our result. [Copyright &y& Elsevier]