Oscillation of the Emden–Fowler Difference Systems

Oscillation Theorems for Symplectic Difference Systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same pr...

Oscillation Criteria for Hamiltonian Matrix Difference Systems

We obtain some oscillation criteria for the Hamiltonian difference system (AY{t) = B{t)Y{t+\) + C{t)Z{t), I AZ{t) = -A{t)Y{t + 1) B*{t)Z{t), where A, B, C, Y, Z are dxd matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.

Symplectic Difference Systems: Oscillation Theory and Hyperbolic Prüfer Transformation

Oscillation criteria for two-dimensional difference systems of first order linear difference equations

Sufficient conditions are established for the oscillation of the linear two-dimensional difference system ∆xn = pn yn, ∆yn−1 = −qnxn, n ∈ N (n0) = {n0, n0 + 1, . . .}, where {pn}, {qn} are nonnegative real sequences. Our results extend the results in the literature. c © 2007 Elsevier Ltd. All rights reserved.

On Some Fractional Systems of Difference Equations

This paper deal with the solutions of the systems of difference equations $$x_{n+1}=frac{y_{n-3}y_nx_{n-2}}{y_{n-3}x_{n-2}pm y_{n-3}y_n pm y_nx_{n-2}}, ,y_{n+1}=frac{y_{n-2}x_{n-1}}{ 2y_{n-2}pm x_{n-1}},,nin mathbb{N}_{0},$$ where $mathbb{N}_{0}=mathbb{N}cup left{0right}$, and initial values $x_{-2},, x_{-1},,x_{0},,y_{-3},,y_{-2},,y_{-1},,y_{0}$ are non-zero real numbers.