The trichotomy for difference systems and applications
The law of large numbers and a functional equation
We deal with the linear functional equation (E) , where g:(0,∞) → (0,∞) is unknown, is a probability distribution, and ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
The maximal solution of a restricted subadditive inequality in numerical analysis.
The method of lower and upper solutions for periodic and anti-periodic difference equations.
The method of variation of parameters in the theory of linear sequences
The multidimensional -transform and its use in solution of partial difference equations
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 robustness of strong stability of positive homogeneous difference equations.
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 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.
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
To the theory of linear difference equations with constant coefficients
Transfer of boundary conditions for difference equations
It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.