Asymptotic Behavior of the Solutions of an nth Order Nonhomogeneous Ordinary Differential Equation

1966 ◽  
Vol 122 (1) ◽  
pp. 177 ◽  
Author(s):  
Thomas G. Hallam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior

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 Some comparison criteria in oscillation theory

1984 ◽  
Vol 36 (2) ◽  
pp. 176-186 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Arbitrary Order ◽  
Oscillation Theory ◽  
Linear Ordinary Differential Equation ◽  
Order Linear ◽  
Comparison Criteria

AbstractThe purpose of this paper is to establish comparison criteria, by which the oscillatory and asymptotic behavior of linear retarded differential equations of arbitrary order is inherited from the oscillation of an associated second order linear ordinary differential equation. These criteria are new even in the case of ordinary differential equations.

Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation

1980 ◽  
Vol 32 (3) ◽  
pp. 631-643 ◽  
Author(s):  
G. F. Webb
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Bounded Domain ◽  
Initial Boundary Value ◽  
Strongly Damped

In this paper we study the nonlinear initial boundary value problem(1.1) ωtt— αΔ ωt— Δω= f(ω), t> 0ω(x, 0) = ϕ(x), x∈ Ωωt(x, 0) = ψ (x), x∈ Ωω(x, t ) = 0, x ∈ ∂Ω, t ≥ 0.In (1.1) Ω is a smooth bounded domain in Rn, n = 1, 2, 3, α > 0, and f ∈ C1(R;R) with f‘(x) ≦ co for all x ∈ R (where c0 is a nonnegative constant), lim sup|x|→+∞f(x)/x ≦0, and f(0) = 0. Our objective will be to establish the existence of unique strong global solutions to (1.1) and investigate their behavior as t→ +∞.Our approach takes advantage of the semilinear character of (1.1) and reformulates the problem as an abstract ordinary differential equation in a Banach space.

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