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On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations

Marian Kwapisz (1993)

Applications of Mathematics

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.

On oscillatory nonlinear fourth-order difference equations with delays

Arun K. Tripathy (2018)

Mathematica Bohemica

In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form Δ 2 ( r ( n ) Δ 2 ( y ( n ) + p ( n ) y ( n - m ) ) ) + q ( n ) G ( y ( n - k ) ) = 0 is studied under the assumption n = 0 n r ( n ) < . New oscillation criteria have been established which generalize some of the existing results in the literature.

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