Boundary Value Problems on Time Scales

Abstract

This volume includes nineteen papers on the relatively recent topic of the study of dynamic equations on a time scale. This theory goes back to its founder Stefan Hilger 1988 , and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete mathematics; moreover, often it revels the reasons for the discrepancies between both theories. This monograph is directed to different kinds of boundary value problems and contains new researches on the existence, uniqueness, and multiplicity of solutions of different types of problems as m-point, p-laplacian, or higher-order equations together with functional and impulsive equations with singularities. The arguments used vary from comparison principles, degree theory or variational methods to approximation theory. In all papers, some physical or medical mathematical models are considered. We would like to express our gratitude to all the participants, who made possible a very stimulating interchange of ideas.