scholarly journals Asymptotic properties of solutions of differential systems with deviating arguments

1990 ◽  
Vol 115 (2) ◽  
pp. 178-191
Author(s):  
Eva Špániková
Keyword(s):  
Asymptotic Properties ◽  
Differential Systems ◽  
Deviating Arguments

scholarly journals On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Youliang Fu ◽  
Yazhou Tian ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Deviating Arguments ◽  
Neutral Delay Differential Equation ◽  
Distributed Deviating Arguments ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

On solutions of third order nonlinear differential equations

2006 ◽  
Vol 4 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Ivan Mojsej ◽  
Ján Ohriska
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Property A ◽  
Comparison Result ◽  
Third Order ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
The Third

AbstractThe aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

scholarly journals Some results on the asymptotic behavior of nonoscillatory solutions of differential equations with deviating arguments

1982 ◽  
Vol 32 (3) ◽  
pp. 295-317 ◽  
Author(s):  
Ch. G. Philos ◽  
Y. G. Sficas ◽  
V. A. Staikos
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
General Setting ◽  
Nonoscillatory Solution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Image Position ◽  
Necessary And Sufficient

AbstractThis paper deals with some asymptotic properties of nonoscillatory solutions of a class of n-th order (n < 1) differential equations with deviationg arguments involving the so called n-th order r-derivative of the unknown function x defined bywhere ri (i = 0,1…n) are positive continous functions on [t0, ∞). The fundamental purpose of this paper is to find for any integer m, 0 < m < n – 1, a necessary and sufficient condition (depending on m) in order that three exists at least one (nonoscillatory) solution x so that the exists in R – {0} The results obtained extend some recent ones due to Philos (1978a) and they prove, in a general setting, the validity of a conjecture made by Kusano and Onose (1975).

scholarly journals Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2552
Author(s):  
Blanka Baculikova
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Second Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
Second Order Differential Equations ◽  
Linear Differential ◽  
New Criteria ◽  
Mixed Argument

In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r(t)(y′(t))α′=p(t)yα(τ(t)). Such differential equation may possesses two types of nonoscillatory solutions either from the class N0 (positive decreasing solutions) or N2 (positive increasing solutions). We establish new criteria for N0=∅ and N2=∅ provided that delayed and advanced parts of deviating argument are large enough. As a consequence of these results, we provide new oscillatory criteria. The presented results essentially improve existing ones even for a linear case of considered equations.

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