A stacked delta-nabla self-adjoint problem of even order

A Stacked Delta-Nabla Self-Adjoint Problem of Even Order

Existence criteria for two positive solutions to a nonlinear, even-order stacked deltanabla boundary value problem with stacked, vanishing conditions at the two endpoints are found using the method of Green’s functions. A few examples are given for standard time scales. The corresponding even-order nabla-delta problem is also discussed in detail. c © 2003 Elsevier Science Ltd. All rights reserv...

Conjugacy of Self-Adjoint Difference Equations of Even Order

and Applied Analysis 3 Let us consider, together with system 2.1 , the matrix linear Hamiltonian system ΔXk AXk 1 BkUk, ΔUk CkXk 1 −AUk, 2.4 where the matrices A,Bk, and Ck are also given by 2.3 . We say that the matrix solution X,U of 2.4 is generated by the solutions y 1 , . . . , y n of 1.1 if and only if its columns are generated by y 1 , . . . , y n , respectively, that is, X,U x y1 , . . ...

The Delta - Nabla Calculus of Variations

The discrete-time, the quantum, and the continuous calculus of variations have been recently unified and extended. Two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we propose a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla r...

Henstock–Kurzweil delta and nabla integrals

We will study the Henstock–Kurzweil delta and nabla integrals, which generalize the Henstock–Kurzweil integral. Many properties of these integrals will be obtained. These results will enable time scale researchers to study more general dynamic equations. The Hensock–Kurzweil delta (nabla) integral contains the Riemann delta (nabla) and Lebesque delta (nabla) integrals as special cases.

Order Properties of Bounded Self-adjoint Operators1