scholarly journals Oscillation of first order linear differential equations with several non-monotone delays

2018 ◽  
Vol 16 (1) ◽  
pp. 83-94
Author(s):  
E.R. Attia ◽  
V. Benekas ◽  
H.A. El-Morshedy ◽  
I.P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

AbstractConsider the first-order linear differential equation with several retarded arguments$$\begin{array}{} \displaystyle x^{\prime }(t)+\sum\limits_{k=1}^{n}p_{k}(t)x(\tau _{k}(t))=0,\;\;\;t\geq t_{0}, \end{array} $$where the functions pk, τk ∈ C([t0, ∞), ℝ+), τk(t) < t for t ≥ t0 and limt→∞τk(t) = ∞, for every k = 1, 2, …, n. Oscillation conditions which essentially improve known results in the literature are established. An example illustrating the results is given.

Oscillation of first-order differential equations with several non-monotone retarded arguments

2020 ◽  
Vol 27 (3) ◽  
pp. 341-350 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Fatma Karakoc ◽  
Gizem S. Oztepe ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Order Linear Differential Equation ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractConsider the first-order linear differential equation with several non-monotone retarded arguments {x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0}, {t\geq t_{0}}, where the functions {p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})}, for every {i=1,2,\ldots,m}, {\tau_{i}(t)\leq t} for {t\geq t_{0}} and {\lim_{t\to\infty}\tau_{i}(t)=\infty}. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

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