Euler type linear and half-linear differential equations and their non-oscillation in the critical oscillation case
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Inequalities and Applications |
| MU Faculty or unit | |
| 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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