First Order Linear Equations

Martin Bohner and Allan Peterson
Additional contact information
Martin Bohner: Univeristy of Missouri-Rolla, Department of Mathematics
Allan Peterson: University of Nebraska, Department of Mathematics

Chapter Chapter 2 in Dynamic Equations on Time Scales, 2001, pp 51-79 from Springer

Abstract: Abstract Definition 2.1. Suppose $$ f:\mathbb{T} \times \mathbb{R}^2 \to \mathbb{R}. $$ Then the equation 2.1 $$ y^\Delta = f(t,y,y^\sigma ) $$ is called a first order dynamic equation, sometimes also a differential equation. If $$ f(t,y,y^\sigma ) = f_1 (t)y + f_2 (t) or f(t,y,y^\sigma ) = f_1 (t)y^\sigma + f_2 (t) $$ for functions f1 and f2, then (2.1) is called a linear equation. A function $$ y: \mathbb{T} \to \mathbb{R} $$ is called a solution of (2.1) if $$ y^\Delta (t) = f(t,y(t),y(\sigma (t))) is satisfied for all t \in \mathbb{T}^\kappa . $$

Keywords: Exponential Function; Dynamic Equation; Adjoint Equation; Generalize Exponential Function; Semigroup Property (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0201-1_2

Ordering information: This item can be ordered from
http://www.springer.com/9781461202011

DOI: 10.1007/978-1-4612-0201-1_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().