In this paper we consider the oscillation of a sixth-order half-linear differential equation for the p-Laplacian like operator with a retarded argument of the form (r(t)|x^(v) (t)|^p-2 x^(v) (t))^' +q(t)|x(τ (t))|^p-2 x(τ(t))=0^. Here the coefficients of the equation satisfy the given conditions. Interest in the study of differential equations with delay is associated with a wide range of applied problems and the development of the theory of ordinary differential equations. The presence of delay in mathematical models and differential equations is a complicating factor, which, as a rule, leads to a narrowing of the stability region of the resulting solutions. The study and solution of ordinary differential equations with delay are comparable in complexity to the study and solution of partial differential equations without delay. To obtain the criterion of oscillation for the equation under consideration, a comparison theorem with a first-order differential equation with delay is proved, to which the previously known oscillatory criterion can be applied.

KOSHKAROVA B.S.

Candidate of Physical and Mathematical Sciences, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

Е-mail: b-koshkarova@yandex.kz, https://orcid.org/0000-0002-0228-4110

ALDAY M.

Candidate of Physical and Mathematical Sciences, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

Е-mail: saiajan@yandex.kz, https://orcid.org/0000-0002-6073-2313

BURGUMBAYEVA S.К.

PhD, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

Е-mail: burgumbayeva_sk@enu.kz, https://orcid.org/0000-0003-2334-7405

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oscillation, half-linear differential equations, p-Laplacian, sixth order, differential equations with delay, comparison theorem