Browsing by Author "Džurina, Jozef"

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Access status: Open Access ,
Oscillatory criteria via linearization of half-linear second order delay differential equations
(Wydawnictwa AGH, 2020) Baculíková, Blanka; Džurina, Jozef
In the paper, we study oscillation of the half-linear second order delay differential equations of the form $\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.$ 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.
Access status: Open Access ,
Oscillatory results for second-order noncanonical delay differential equations
(Wydawnictwa AGH, 2019) Džurina, Jozef; Jadlovská, Irena; Stavroulakis, Ioannis P.
The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation $\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,$ under the condition $\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.$ Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.
Access status: Open Access ,
Properties of even order linear functional differential equations with deviating arguments of mixed type
(Wydawnictwa AGH, 2022) Džurina, Jozef
This paper is concerned with oscillatory behavior of linear functional differential equations of the type $y^{(n)}(t)=p(t)y(\tau(t))$ with mixed deviating arguments which means that its both delayed and advanced parts are unbounded subset of $(0,\infty)$. Our attention is oriented to the Euler type of equation, i.e. when $p(t)\sim a/t^n.$