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Solvability of a Higher‐Order Three‐Point Boundary Value Problem on Time Scales

Yanbin Sang

Abstract and Applied Analysis, 2009, vol. 2009, issue 1

Abstract: We consider a higher‐order three‐point boundary value problem on time scales. A new existence result is first obtained by using a fixed point theorem due to Krasnoselskii and Zabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficient conditions for the existence of a nonnegative and nontrivial solution are obtained by using Leray‐Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easy to verify; as an application, some examples to demonstrate our results are given.

Date: 2009
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https://doi.org/10.1155/2009/341679

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