Leonid Berezansky, Department of Mathematics, Ben Gurion University of the Negev, P.O.Box 653, Beer Sheva 8410501, Israel, e-mail: brznsky@cs.bgu.ac.il; Sandra Pinelas, Academia Militar, Departamento de Ciencias Exactas e Naturais, Avenide Conde Castro Guimaraes, 2720-113 Amadora, Portugal, e-mail: sandra.pinelas@gmail.com
Abstract: The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type
$$\Delta x(n)+\sum_{k=-p}^qa_k(n)x(n+k)=0,\quad n>n_0,$$
where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\{a_k(n)\}$ are sequences of real numbers for $k=-p,\ldots,q$, and $p>0$, $q\geq0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.
Keywords: oscillation; difference equation; mixed type; asymptotic behavior
Classification (MSC 2010): 39A21, 39A99
DOI: 10.21136/MB.2016.14
Full text available as PDF.
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 myris@myris.cz.