Asymptotic properties of solutions to fourth order difference equations

[摘要] We consider equations of the form Delta(2)(r(n)Delta(2)x(n)) = a(n)f (x(sigma(n))) + b(n), where a, b are sequences of real numbers, r is a sequence of positive real numbers, sigma a sequence of integers. Let Y denote the space of all solutions of the equation Delta(2)(r(n)Delta(2)y(n)) = 0, and let s be a fixed nonpositive real number. We present sufficient conditions under which for a given sequence y is an element of Y there exists a solution x with the asymptotic behavior x(n) = y(n) + o(n(s)). Moreover, we establish conditions under which for a given solution x there exists a sequence y is an element of Y such that x has the above asymptotic behavior. The obtained results are applied to the study of solutions of discrete Euler-Bernoulli beam equation. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-15

[关键词] Fourth order difference equations;Euler-Bernoulli beam equation;Prescribed asymptotic behavior;Bounded solution;Convergent solution