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Non-oscillation of modified Euler type linear and half-linear differential equations

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Abstract

Modified Euler type second order half-linear differential equations are considered and a non-oscillation criterion is derived for them. This criterion is the counterpart of a previously obtained oscillation theorem. Thus, from the main result of this paper, it follows that the studied equations are conditionally oscillatory in a very general case. To prove the non-oscillation criterion, a combination of the Riccati technique and the generalized Prüfer angle is used. Since the criterion is new in many cases (especially, in the linear case), several corollaries are formulated and the novelty is illustrated by an example as well.

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Acknowledgements

The author would like to thank the reviewers for valuable comments that improved the final version of this paper.

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  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Jiřina Šišoláková

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Correspondence to Jiřina Šišoláková.

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This work was supported from Operational Programme Research, Development and Education—“Project Internal Grant Agency of Masaryk University”, No. CZ.02.2.69/0.0/0.0/19\(\_\)073/0016943.

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Šišoláková, J. Non-oscillation of modified Euler type linear and half-linear differential equations. European Journal of Mathematics 8, 700–721 (2022). https://doi.org/10.1007/s40879-021-00522-4

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