An improved product type oscillation test for partial difference equations. (English) Zbl 1472.39016
Summary: We present new oscillation tests for the \(\mathrm{P}\Delta\mathrm{E}\)
\[
a u (m + 1, n) + b u (m, n + 1) - c u (m, n) + p (m, n) u (m - \tau, n - \sigma) = 0,\ m, n = 0, 1, \dots,
\]
where \(a, b, c \in (0, \infty)\) and \(\tau, \sigma \in\{0, 1, \dots \}\), and \(\{p(m, n)\} \subset [0, \infty)\). Our main result improves some of the well-known results in the literature. We also present a numerical example, where all the previous results in the literature fail to deliver an answer.
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