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We deal with the linear functional equation (E) $g (x) = \sum_{i = 1}^{r} p_{i} g (c_{i} x)$ , where g:(0,∞) → (0,∞) is unknown, $(p ₁, . . ., p_{r})$ is a probability distribution, and $c_{i}$ ’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.

Roger J. Wallace (1987)

Aequationes mathematicae

The method of lower and upper solutions for periodic and anti-periodic difference equations.

Cabada, Alberto (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

The method of variation of parameters in the theory of linear sequences

Miroslav Laitoch (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The multidimensional $z$ -transform and its use in solution of partial difference equations

Jiří Gregor (1988)

Kybernetika

The oscillation of an $m$ th order perturbed nonlinear difference equation

Patricia J. Y. Wong, Ravi P. Agarwal (1996)

Archivum Mathematicum

We offer sufficient conditions for the oscillation of all solutions of the perturbed difference equation $| Δ^{m} {y (k) |}^{α - 1} Δ^{m} y (k) + Q (k, y (k - σ_{k}), Δ y (k - σ_{k}), \dots, Δ^{m - 2} y (k - σ_{k}))$ $= P (k, y ...$

The periodic character of the difference equation $x_{n + 1} = f (x_{n - l + 1}, x_{n - 2 k + 1})$ .

Sun, Taixiang, Xi, Hongjian (2008)

Advances in Difference Equations [electronic only]

The periodic solutions of the second order nonlinear difference equation.

Ryszard Musielak, Jerzy Popenda (1988)

Publicacions Matemàtiques

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

Marco Ferrante (1996)

Rendiconti del Seminario Matematico della Università di Padova

The robustness of strong stability of positive homogeneous difference equations.

Bui, The Anh, Duong, Dang Xuan Thanh (2008)

Journal of Applied Mathematics

Thermodynamic modeling, energy equipartition, and nonconservation of entropy for discrete-time dynamical systems.

Haddad, Wassim M., Hui, Qing, Nersesov, Sergey G., Chellaboina, Vijaysekhar (2005)

Advances in Difference Equations [electronic only]

Third-order nonlocal problems with sign-changing nonlinearity on time scales.

Anderson, Douglas R., Tisdell, Christopher C. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Three solutions to Dirichlet boundary value problems for $p$ -Laplacian difference equations.

Jiang, Liqun, Zhou, Zhan (2008)

Advances in Difference Equations [electronic only]

Three solutions to discrete anisotropic problems with two parameters

Marek Galewski, Piotr Kowalski (2014)

Open Mathematics

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

C. O. A. Sowunmi (2003)

Banach Center Publications

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].

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