Linear even order homogenous difference equation with delay in coefficient

• Autoři: JEKL Jan
• Rok publikování: 2020
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Electronic Journal of Qualitative Theory of Differential Equations
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: 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
• Klíčová slova: coefficient delayed equations; separately disconjugate; oscillation theory; minimal solution; difference equation
• Popis: 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.

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