Geodesic
Oscillation properties for a scalar linear difference equation of mixed type
Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 169-182.

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The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type $$ \Delta x(n)+\sum _{k=-p}^{q}a_{k}(n)x(n+k)=0,\quad n>n_{0}, $$ 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 $p>0$, $q\geq 0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.
DOI : 10.21136/MB.2016.14
Classification : 39A21, 39A99
Keywords: oscillation; difference equation; mixed type; asymptotic behavior 
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Berezansky, Leonid; Pinelas, Sandra. Oscillation properties for a scalar linear difference equation of mixed type. Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 169-182. doi : 10.21136/MB.2016.14. http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.14/

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