On continuous dependence of solutions of linear differential equations on a parameter in a Banach space

1999 ◽  
Vol 51 (2) ◽  
pp. 311-318
Author(s):  
Fam Ngok Boi ◽  
Nguyen Tkhe Hoan
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Continuous Dependence ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Continuous Dependence Of Solutions

CONTINUITY OF ROOTS, REVISITED

2018 ◽  
Vol 98 (3) ◽  
pp. 448-455
Author(s):  
DARIUSZ BUGAJEWSKI ◽  
PIOTR MAĆKOWIAK
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Linear Differential Equations ◽  
Topological Proof ◽  
Constant Coefficients ◽  
Roots Of Polynomials ◽  
Linear Differential ◽  
Continuous Dependence Of Solutions

The aim of this note is to give a simple topological proof of the well-known result concerning continuity of roots of polynomials. We also consider a more general case with polynomials of a higher degree approaching a given polynomial. We then examine the continuous dependence of solutions of linear differential equations with constant coefficients.

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