Non-oscillation of half-linear differential equations with periodic coefficients

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Authors	VESELÝ Michal HASIL Petr
Year of publication	2015
Type	Article in Periodical
Magazine / Source	Electronic Journal of Qualitative Theory of Differential Equations
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=3311
Doi	http://dx.doi.org/10.14232/ejqtde.2015.1.1
Field	General mathematics
Keywords	half-linear equations; Euler type equations; oscillation theory; conditional oscillation; oscillation constant
Description	We consider half-linear Euler type differential equations with general periodic coefficients. It is well-known that these equations are conditionally oscillatory, i.e., there exists a border value given by their coefficients which separates oscillatory equations from non-oscillatory ones. In this paper, we study oscillatory properties in the border case. More precisely, we prove that the considered equations are non-oscillatory in this case. Our results cover the situation when the periodic coefficients do not have any common period.
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