A Note on Transformations of Independent Variable in Second Order Dynamic Equations

被引：1
|
作者：
Rehak, Pavel [1 ]
机构：
[1] Brno Univ Technol, Inst Math, FME, Tech 2, Brno 61669, Czech Republic
来源：
DIFFERENCE EQUATIONS AND DISCRETE DYNAMICAL SYSTEMS WITH APPLICATIONS, ICDEA 2018 | 2020年 / 312卷
关键词：
Transformation; Chain rule; Dynamic equation; Time scale; Oscillation; Asymptotic formulae; DIFFERENTIAL-EQUATIONS; SYSTEMS;
D O I：
10.1007/978-3-030-35502-9_15
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The main purpose of this paper is to show how a transformation of independent variable in dynamic equations combined with suitable statements on a general time scale can yield new results or new proofs to known results. It seems that this approach has not been extensively used in the literature devoted to dynamic equations. We present, in particular, two types of applications. In the first one, an original dynamic equation is transformed into a simpler equation. In the second one, a dynamic equation in a somehow critical setting is transformed into a noncritical case. These ideas will be demonstrated on problems from oscillation theory and asymptotic theory of second order linear and nonlinear dynamic equations.
引用
收藏
页码：335 / 353
页数：19
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