J-self-adjoint extensions for second-order linear difference equations with complex coefficients

Homoclinic orbits for second order self-adjoint difference equations

In this paper we discuss how to use variational methods to study the existence of nontrivial homoclinic orbits of the following nonlinear difference equations Δ [ p(t)Δu(t − 1)]+ q(t)u(t)= f (t, u(t)), t ∈Z, without any periodicity assumptions on p(t), q(t) and f , providing that f (t, x) grows superlinearly both at origin and at infinity or is an odd function with respect to x ∈R, and satisfie...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Plancherel-Rotach asymptotics of second-order difference equations with linear coefficients

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 , . . ...

On Self-Adjoint Differential Equations of Second Order.