Abstract
We consider the boundary value problem where n ⩾ 2 and m ⩾ 1 are integers, tj ∈ [0, 1] for j = 1, …, m, and f and gi, i = 0, …, n − 1, are continuous. We obtain sufficient conditions for the existence of a solution of the above problem based on the existence of lower and upper solutions. Explicit conditions are also found for the existence of a solution of the problem. The differential equation has dependence on all lower order derivatives of the unknown function, and the boundary conditions cover many multi-point boundary conditions studied in the literature. Schauder’s fixed point theorem and appropriate Nagumo conditions are employed in the analysis. Examples are given to illustrate the results. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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