MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 19-33, 2005

On the oscillation of solutions of third order linear difference equations of neutral type

Anna Andruch-Sobilo, Malgorzata Migda

Anna Andruch-Sobilo, Malgorzata Migda, Institute of Mathematics, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland, e-mail:,

Abstract: In this note we consider the third order linear difference equations of neutral type
\label{E} \Delta^3[x(n)-p(n)x(\sigma(n))]+\delta q(n)x(\tau(n))=0, \quad n \in N(n_0), \tag{$ E$}
where $\delta=\pm1$, $p,q N(n_0)\rightarrow\bb R_+;$ $\sigma,\tau N(n_0)\rightarrow\bb N$, $\lim_{n \rightarrow\infty}\sigma(n)= \lim\limits_{n \rightarrow\infty}\tau(n)= \infty.$ We examine the following two cases:
\align\{0<p(n)&\leq1, \sigma(n)=n+k, \tau(n)=n+l\},
\{p(n)&>1, \sigma(n)=n-k, \tau(n)=n-l\},
where $k$, $l$ are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.

Keywords: neutral type difference equation, nonoscillatory solution, asymptotic behavior

Classification (MSC 2000): 39A11

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at

[Previous Article] [Next Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]