The oscillation of an th order perturbed nonlinear difference equation
We offer sufficient conditions for the oscillation of all solutions of the perturbed difference equation
The periodic character of the difference equation .
The periodic solutions of the second order nonlinear difference equation.
Periodic and asymptotically periodic solutions of the nonlinear equation Δ2xn + anf(xn) = 0, n ∈ N, are studied.
The Picard boundary value problem for a third order stochastic difference equation
The rational qKZ equation and shifted non-symmetric Jack polynomials.
The robustness of strong stability of positive homogeneous difference equations.
The spectral matrices of Toda solitons and the fundamental solution of some discrete heat equations
The Stieltjes spectral matrix measure of the doubly infinite Jacobi matrix associated with a Toda -soliton is computed, using Sato theory. The result is used to give an explicit expansion of the fundamental solution of some discrete heat equations, in a series of Jackson’s -Bessel functions. For Askey-Wilson type solitons, this expansion reduces to a finite sum.
The stability analysis of a discretized pantograph equation
The paper deals with a difference equation arising from the scalar pantograph equation via the backward Euler discretization. A case when the solution tends to zero but after reaching a certain index it loses this tendency is discussed. We analyse this problem and estimate the value of such an index. Furthermore, we show that the utilized proof technique enables us to investigate some other numerical formulae, too.
The stability cone for a matrix delay difference equation.
The zero distribution and uniqueness of difference-differential polynomials
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems.
Third-order nonlocal problems with sign-changing nonlinearity on time scales.
Three positive solutions for -Laplacian functional dynamic equations on time scales.
Three solutions for a discrete nonlinear Neumann problem involving the -Laplacian.
Three solutions to Dirichlet boundary value problems for -Laplacian difference equations.
Three solutions to discrete anisotropic problems with two parameters
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem.
Time discrete 2-sex population model
A time-discrete 2-sex model with gestation period is analysed. It is significant that the conditions for local stability of a nontrivial steady state do not require that the expected number of female offspring per female equal unity. This is in contrast to results obtained by Curtin and MacCamy [4] and the author [10].
Time-scale integral inequalities.
To the theory of linear difference equations