Oscillation behavior of second-order self-adjoint $ q $-difference equations

In this study, we investigate the oscillation behavior of second-order self-adjoint $ q $-difference equations, focusing on the renowned Leighton oscillation theorem. Through an example, we demonstrate that the $ q $-version of Leighton's classical oscillation theorem does not hold and requires...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 16876 - 16884
Main Authors Zafer, Aǧacık, Gürkan, Zeynep Nilhan
Format Journal Article
LanguageEnglish
Published AIMS Press 2024
Subjects
oscillation
q $-difference
quantum calculus
second-order equation
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024819

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Summary:In this study, we investigate the oscillation behavior of second-order self-adjoint $ q $-difference equations, focusing on the renowned Leighton oscillation theorem. Through an example, we demonstrate that the $ q $-version of Leighton's classical oscillation theorem does not hold and requires refinement. To address this, we introduce an oscillation-preserving transformation and establish alternative theorems to the ones existing in the literature. The strength of our work lies in the absence of any sign condition on the potential function. We also provide illustrative examples to support our findings and mention directions for future research.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024819