Two-point boundary value problems on in-homogeneous time-scale dynamic processes (Q1330998)

In the paper are described some salient features of time-scales (i.e. closed subsets of \(\mathbb{R}\)), functions defined on time-scales, operations with those functions and the qualitative theory of linear dynamic processes. The variation of parameters formula is presented and a few notions on boundary value problems. The main result concerns the existence and uniqueness of solutions to two-point boundary value problems on an inhomogeneous time-scale of a system of the linear dynamic process. The properties of corresponding Green's matrix are also discussed. Moreover, a generalization of the obtained results to multipoint boundary value problems is given.