Terminal value problems for first and second order nonlinear equations on time scales.
The complete polynomial grid
The convolution on time scales.
The direct Lyapunov method for an almost periodic difference system on a compactum.
The discrete Beverton-Holt model with periodic harvesting in a periodically fluctuating environment.
The discrete version of Ostrowski's inequality in normed linear spaces.
The entire solutions of a polynomial difference equation.
The formulation of second-order boundary value problems on time scales.
The General Solution of Some Finite Difference Equations Analogous to the Wave Equation.
The Green formula and HP Spaces on trees.
The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix
A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries taken from the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hull of the canonical basis in ℓ2(ℤ+) are essentially self-adjoint for |ν| ≥ 1 and have deficiency indices (1, 1) for |ν| < 1. A convenient description of all self-adjoint extensions is obtained and the spectral problem is analyzed in detail. The spectrum is discrete and the characteristic equation...
The Helmholtz conditions for the difference equations systems.
The trichotomy for difference systems and applications
The laplacian and the discrete laplacian
The lattice structure of connection preserving deformations for -Painlevé equations I.
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