Publication details

Euler type linear and half-linear differential equations and their non-oscillation in the critical oscillation case

Authors

DOŠLÁ Zuzana HASIL Petr MATUCCI Serena VESELÝ Michal

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Inequalities and Applications
MU Faculty or unit

Faculty of Science

Citation
Web https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-019-2137-0
Doi http://dx.doi.org/10.1186/s13660-019-2137-0
Keywords Half-linear equations; Linear equations; Euler type equations; Oscillation theory; Oscillation criterion; Non-oscillation criterion; Oscillation constant; p-Laplacian
Description This paper is devoted to the analysis of the oscillatory behavior of Euler type linear and half-linear differential equations. We focus on the so-called conditional oscillation, where there exists a borderline between oscillatory and non-oscillatory equations. The most complicated problem involved in the theory of conditionally oscillatory equations is to decide whether the equations from the given class are oscillatory or non-oscillatory in the threshold case. In this paper, we answer this question via a combination of the Riccati and Prüfer technique. Note that the obtained non-oscillation of the studied equations is important in solving boundary value problems on non-compact intervals and that the obtained results are new even in the linear case.
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