Asymptotic properties of Kneser type solutions for third order half-linear neutral difference equations

[摘要] The authors examine properties of positive solutions of the third order half-linear neutral difference equation \begin{equation*} \Delta(a_n\Delta(b_n(\Delta z_n)^{\alpha}))+q_ny_{n+1}^{\alpha}=0, \end{equation*} where $z_n=y_n+p_ny_{\sigma(n)}$. They show that the positive solutions are in fact Kneser type solutions and they provide upper and lower bounds that yield the rate of convergence to zero for such solutions. Examples are provided to illustrate the main results.

[学科分类] 数学（综合）

[关键词] difference equations;third order;half-linear;Kneser solutions;nonoscillation