Asymptotic behavior of solutions of Cauchy relaxed problem for a differential equation with unbounded operator in a Banach space

1989 ◽  
Vol 41 (6) ◽  
pp. 654-659
Author(s):  
G. K. Roginskii
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Asymptotic Behavior ◽  
Unbounded Operator ◽  
Asymptotic Behavior Of Solutions ◽  
Relaxed Problem

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.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

scholarly journals Asymptotic Behavior of Solutions of Even-Order Advanced Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Omar Bazighifan ◽  
Hijaz Ahmad
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Second Order ◽  
Asymptotic Behavior Of Solutions ◽  
Qualitative Behavior ◽  
Riccati Transformation ◽  
Even Order ◽  
Second Order Equations

In this paper, we establish the qualitative behavior of the even-order advanced differential equation a υ y κ − 1 υ β ′ + ∑ i = 1 j q i υ g y η i υ = 0 ,   υ ≥ υ 0 . The results obtained are based on the Riccati transformation and the theory of comparison with first- and second-order equations. This new theorem complements and improves a number of results reported in the literature. Two examples are presented to demonstrate the main results.

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