Publication details

Prüfer angle and non-oscillation of linear equations with quasiperiodic data

Authors

HASIL Petr VESELÝ Michal

Year of publication 2019
Type Article in Periodical
Magazine / Source MONATSHEFTE FUR MATHEMATIK
MU Faculty or unit

Faculty of Science

Citation
Web Full Text
Doi http://dx.doi.org/10.1007/s00605-018-1232-5
Keywords Sturm-Liouville equation; Prüfer angle; oscillation theory; periodic coefficient; non-oscillation
Description We consider the Sturm-Liouville differential equations with a power of the independent variable and sums of periodic functions as coefficients (including the case when the periodic coefficients do not have any common period). Using known results, one can show that the studied equations are conditionally oscillatory, i.e., there exists a threshold value which can be expressed by the coefficients and which separates oscillatory equations from non-oscillatory ones. It is very complicated to specify the behaviour of the treated equations in the borderline case. In this paper, applying the method of the modified Prüfer angle, we answer this question and we prove that the considered equations are non-oscillatory in the critical borderline case.
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