Non-oscillation criterion for Euler type half-linear difference equations with consequences in linear case

Hasil, Petr; Pospíšil, Michal; Šišoláková, Jiřina; Veselý, Michal

doi:10.1007/s10474-022-01218-1

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…Now, we explicitly collect the basic motivation for our results by the selected theorems mentioned below. The strongest known oscillation results about the analyzed Euler type difference equations are proved in [3][4][5][6][7][8][9][10] (some important partial cases of these results are proved in [11][12][13][14]; see also [15] for a basic result). We remark that we unify the forms of the results below.…”

Section: Motivationmentioning

confidence: 99%

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Oscillation criterion for Euler type half‐linear difference equations

Hasil,

Veselý

2023

Math Methods in App Sciences

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We consider general classes of Euler type linear and half‐linear difference equations, which are conditionally oscillatory. Applying the adapted Riccati technique, we improve known oscillation criteria for these equations. More precisely, our presented main criterion is the full oscillatory counterpart of a non‐oscillation criterion. Thus, in this paper, we enlarge the set of conditionally oscillatory Euler type difference equations. We highlight that our results are new even for linear equations with periodic coefficients. This fact is documented by simple examples of such equations at the end of this paper.

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Section: Motivationmentioning

confidence: 99%

“…Theorem 4 combines the strongest known relevant non‐oscillation criteria. In the following two theorems, we give the corresponding strongest known oscillation criteria (for illustrative examples, see [8, Examples 1–3] together with [3, Examples 3.4 and 3.6]).…”

Section: Preliminaries and Motivationmentioning

confidence: 99%