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 andZabreiko. Later, under certain growth conditions imposed on the nonlinearity, several sufficientconditions for the existence of a nonnegative and nontrivial solution are obtained by usingLeray-Schauder nonlinear alternative. Our conditions imposed on nonlinearity are all very easyto verify; as an application, some examples to demonstrate our results are given.
"Solvability of a Higher-Order Three-Point Boundary Value Problem on Time Scales." Abstr. Appl. Anal. 2009 1 - 16, 2009. https://doi.org/10.1155/2009/341679