1 results
Upper and lower limit oscillation conditions for first-order difference equations
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 3 / August 2022
- Published online by Cambridge University Press:
- 07 July 2022, pp. 618-631
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- Article
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In this work, we consider the first-order difference equation with general argument
\[ \varDelta x(n)+p(n)x\left( \tau (n)\right) =0,\quad n\geq 0, \]where $(p(n))$
is a sequence of non-negative real numbers, $(\tau (n))$
is a sequence of integers such that $\tau (n)< n$
for$\ n\in \mathbf {N},\,$
and$\ \lim _{n\rightarrow \infty }\tau (n)=\infty.$
Under the assumption that the deviating argument is not necessarily monotone, we obtain some new oscillation conditions and improve the all known results for the above equation in the literature, involving only upper and only lower limit conditions. Two examples illustrating the results are also given.
