On the asymptotic behavior of the spectral function of a selfadjoint differential equation of the second order and on expansion in eigenfunctions. II

1977 ◽  
pp. 165-188 ◽  
Author(s):  
B. M. Levitan
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Spectral Function ◽  
Second Order ◽  
Expansion In Eigenfunctions

scholarly journals Positive decreasing solutions of second order quasilinear ordinary differential equations in the framework of regular variation

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 1995-2010 ◽  
Author(s):  
Jelena Milosevic ◽  
Jelena Manojlovic
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Analysis ◽  
Ordinary Differential Equations ◽  
Regular Variation ◽  
Second Order ◽  
Precise Information ◽  
Varying Coefficients

This paper is concerned with asymptotic analysis of positive decreasing solutions of the secondorder quasilinear ordinary differential equation (E) (p(t)?(|x'(t)|))'=q(t)?(x(t)), with the regularly varying coefficients p, q, ?, ?. An application of the theory of regular variation gives the possibility of determining the precise information about asymptotic behavior at infinity of solutions of equation (E) such that lim t?? x(t)=0, lim t?? p(t)?(-x'(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.

scholarly journals On Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Damped Neutral Differential Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ercan Tunç ◽  
Said R. Grace
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations

This paper discusses oscillatory and asymptotic properties of solutions of a class of second-order nonlinear damped neutral differential equations. Some new sufficient conditions for any solution of the equation to be oscillatory or to converge to zero are given. The results obtained extend and improve some of the related results reported in the literature. The results are illustrated with examples.

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