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

Investor logo

Warning

This publication doesn't include Faculty of Education. It includes Faculty of Science. Official publication website can be found on muni.cz.
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.