Linear even order homogenous difference equation with delay in coefficient

Warning

This publication doesn't include Faculty of Sports Studies. It includes Faculty of Science. Official publication website can be found on muni.cz.

Authors	JEKL Jan
Year of publication	2020
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=8213
Doi	https://doi.org/10.14232/ejqtde.2020.1.45
Keywords	coefficient delayed equations; separately disconjugate; oscillation theory; minimal solution; difference equation
Description	We use many classical results known for the self-adjoint second-order linear equation and extend them for a three-term even order linear equation with a delay applied to coefficients. We derive several conditions concerning the oscillation and the existence of positive solutions. Our equation for a choice of parameter is disconjugate, and for a different choice can have positive and oscillatory solutions at the same time. However, it is still, in a sense, disconjugate if we use a weaker definition of oscillation.
Related projects:	Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace Matematické struktury 9