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Browsing by Subject "neutral difference equation"

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    Item type:Article, Access status: Open Access ,
    Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations
    (2006) Migda, Małgorzata
    In this paper we study asymptotic behavior of solutions of a higher order neutral difference equation of the form $\Delta^m(x_n+p_nx_{n-\tau})+f(n,x_{\sigma (n)})=h_n.$ We present conditions under which all nonoscillatory solutions of the above equation have the property $x_n = cn^{m-1}+o(n^{m-1})$ for some $c\in R$.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Oscillation criteria for even order neutral difference equations
    (Wydawnictwa AGH, 2019) Selvarangam, Srinivasan; Rupadevi, S. A.; Thandapani, Ethiraju; Pinelas, Sandra
    In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form $\Delta^m(x_n+ax_{n-\tau_1}+bx_{n+\tau_2})+p_nx_{n-\sigma_1}^{\alpha}+q_nx_{n+\sigma_2}^{\beta}=0,\quad n\geq n_0\gt0,$ where $m\geq 2$ is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.