On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type is given.
We consider linear difference equations whose coefficients are meromorphic at . We characterize the meromorphic equivalence classes of such equations by means of a system of meromorphic invariants. Using an approach inspired by the work of G. D. Birkhoff we show that this system is free.
In the paper a modification of Samoilenko's numerical analytic method is adapted for solving of boundary value problems for difference equation. Similarly to the case of differential equations it is shown that the considered modification of the method requires essentially less restrictive condition-then the original method-for existence and uniqueness of solution of auxiliary equations which play a crucial role in solving the boundary value problems for difference equations.