Oscillation of fourth order nonlinear neutral difference equations-II

Mathematica Slovaca

A. Tripathy¹ 

关键词: oscillation;    non-oscillation;    neutral difference equations;    existence of positive solutions;    asymptotic behaviour;   

DOI  :  10.2478/s12175-008-0095-y

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Oscillatory and asymptotic behaviour of solutions of a class of fourth order nonlinear neutral difference equations of the form $$Delta ^2 (r(n)Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = 0$$ and $$(E) Delta ^2 (r(n)Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = f(n)$$ are studied under the assumption $$sumlimits_{n = 0}^infty {frac{n}{{r(n)}}} $$ < ∞, for different ranges of p(n). Sufficient conditions are obtained for the existence of positive bounded solutions of (E).

【 授权许可】

Unknown