MMN-3612

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

**R. Srinivasan**, SRM University, Department of Mathematics, Ramapuram Campus, Chennai 600 089, India,`srinimaths1986@gmail.com`

**C. Dharuman**, SRM University, Department of Mathematics, Ramapuram Campus, Chennai 600 089, India,`cdharuman55@gmail.com`

**John R. Graef**, University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA,`John-Graef@utc.edu`

**E. Thandapani**, University of Madras, Ramanujan Inst. for Advanced Study in Math., Chennai 600 005, India,`ethandapani@yahoo.co.in`

## Abstract

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.

Vol. 22 (2021), No. 2, pp. 991-1000

DOI: 10.18514/MMN.2021.3612