Linear even order homogenous difference equation with delay in coefficient

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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	http://dx.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