Solvability of a higher-order three-point boundary value problem on time scales (Q963151)

Summary: 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 the 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.