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Properties of even order linear functional differential equations with deviating arguments of mixed type

Dzurina Jozef

Opuscula Mathematica

2022

Vol. 42, no. 5

659--671

This paper is concerned with oscillatory behavior of linear functional differential equations of the type y(n)(t) = p(t)y(τ (t)) with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of (0,∞). Our attention is oriented to the Euler type of equation, i.e. when p(t) ∼ a/tn.

Oscillation of even order linear functional differential equations with mixed deviating arguments

Baculikova Blanka

Opuscula Mathematica

2022

Vol. 42, no. 4

549--560

In the paper, we study oscillation and asymptotic properties for even order linear functional differential equations y (n)(t) = p(t)y(τ (t)) with mixed deviating arguments, i.e. when both delayed and advanced parts of τ (t) are significant. The presented results essentially improve existing ones.

Oscillatory criteria via linearization of half-linear second order delay differential equations

Baculikova Blanka, Dzurina Jozef

Opuscula Mathematica

2020

Vol. 40, no. 5

523--536

In the paper, we study oscillation of the half-linear second order delay differential equations of the form [formula]. We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.