we study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which… (More)

Abstract This article investigates both basic qualitative and basic quantitative properties of solutions to first– and higher–order dynamic equations on time scales and thus provides a foundation and… (More)

Abstract This article introduces the basic qualitative and basic quantitative theory of Volterra integral equations on time scales and thus may be considered as a foundation for future advanced… (More)

where F : T × R → CK(R) is a set-valued map and g : T × T → R is a single-valued continuous map (CK(R) denotes the set of nonempty, closed, and convex subsets of R). In Section 3 some general… (More)

In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas… (More)

Oscillation and nonoscillation properties of second order Sturm–Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order… (More)

This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order dynamic equations on time scales subject to two-point boundary conditions. The… (More)

subject to the initial condition xðt0Þ 1⁄4 x0; t0 $ 0; x0 [ R; ð2Þ where f : 1⁄20;1Þ £ R ! R is a continuous function and t is from a so-called “time scale” T (which is a nonempty closed subset of… (More)

We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green’s functions, we prove the… (More)