scholarly journals Asymptotic behavior of solutions of a first-order impulsive neutral differential equation in Euler form

2011 ◽  
Vol 24 (7) ◽  
pp. 1218-1224 ◽  
Author(s):  
Kaizhong Guan ◽  
Jianhua Shen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Neutral Differential Equation ◽  
Asymptotic Behavior Of Solutions ◽  
First Order ◽  
Euler Form

Oscillation of first order neutral differential equations of Euler form

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Kaizhong Guan ◽  
Jianhua Shen
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Unbounded Delay ◽  
Euler Form

In this paper, we investigate the first order neutral differential equation of Euler form with variable unbounded delaywhere 0 ≤

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

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