New monotonicity properties and oscillation of n-order functional differential equations with deviating argument

Baculíková, Blanka (2023) New monotonicity properties and oscillation of n-order functional differential equations with deviating argument. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (30). pp. 1-10. ISSN 1417-3875

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Abstract

In this paper, we offer new technique for investigation of the even order linear differential equations of the form y(n)(t) = p(t)y(τ(t)). (E) Weestablish new criteria for bounded and unbounded oscillation of (E) which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicities for the positive solutions of (E) than those presented in known works. We illustrate the improvement over known results by applying and comparing our technique with the other known methods on the particular examples.

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