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

الملخص EN

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.