On the Monotone Solutions of Some ODEs. I: Structure of the Solutions

2006 ◽  
pp. 271-277
Author(s):  
Tadie
Keyword(s):  
Monotone Solutions

scholarly journals Connecting Orbit Structure of Monotone Solutions in the Shadow System

1997 ◽  
Vol 140 (2) ◽  
pp. 309-364 ◽  
Author(s):  
Hiroshi Kokubu ◽  
Konstantin Mischaikow ◽  
Yasumasa Nishiura ◽  
Hiroe Oka ◽  
Takeshi Takaishi
Keyword(s):  
Shadow System ◽  
Orbit Structure ◽  
Connecting Orbit ◽  
Monotone Solutions

Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations

1981 ◽  
Vol 90 (1-2) ◽  
pp. 25-40 ◽  
Author(s):  
Takaŝi Kusano ◽  
Manabu Naito ◽  
Kyoko Tanaka
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Solution Space ◽  
Extreme Situation ◽  
Nonoscillatory Solutions ◽  
Linear Ordinary Differential Equations ◽  
Image Position ◽  
Monotone Solutions

SynopsisThe equation to be considered iswhere pi(t), 0≦i≦n, and q(t) are continuous and positive on some half-line [a, ∞). It is known that (*) always has “strictly monotone” nonoscillatory solutions defined on [a, ∞), so that of particular interest is the extreme situation in which such strictly monotone solutions are the only possible nonoscillatory solutions of (*). In this paper sufficient conditions are given for this situation to hold for (*). The structure of the solution space of (*) is also studied.

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