Nonoscillatory solutions of linear differential equations with deviating arguments

1984 ◽  
Vol 136 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Manabu Naito
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Linear Differential

Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments

1978 ◽  
Vol 81 (3-4) ◽  
pp. 195-210 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Unknown Function ◽  
Continuous Functions ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

SynopsisThis paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined bywhere r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.

Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Linear Differential

AbstractIn this paper we derive oscillation criteria for the second order half-linear neutral differential equationwhere Φ(

scholarly journals Asymptotics of some classes of nonoscillatory solutions of second-order half-linear differential equations

2003 ◽  
Vol 127 (28) ◽  
pp. 61-74
Author(s):  
Kusano Takasi ◽  
Vojislav Maric ◽  
Tomoyuki Tanigawa
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Second Order ◽  
Linear Differential Equations ◽  
Nonoscillatory Solutions ◽  
Linear Differential ◽  
Precise Asymptotic

The precise asymptotic behaviour at infinity of some classes of nonoscillatory solutions of the half-linear differential equations is determined.

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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