scholarly journals The Cauchy problem for weakly hyperbolic systems of linear differential equations with constant coefficients

1966 ◽  
Vol 091 (4) ◽  
pp. 431-452
Author(s):  
Jiří Kopáček ◽  
Marie Suchá
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Hyperbolic Systems ◽  
Linear Differential Equations ◽  
The Cauchy Problem ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Weakly Hyperbolic Systems

scholarly journals The behavior of solutions of non-linear differential equations in Hilbert space. I

1988 ◽  
Vol 11 (1) ◽  
pp. 143-165 ◽  
Author(s):  
Vladimir Schuchman
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Differential Equations ◽  
Linear Case ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Linear Differential ◽  
Degenerate Linear

This paper deals with the behavior of solutions of ordinary differential equations in a Hilbert Space. Under certain conditions, we obtain lower estimates or upper estimates (or both) for the norm of solutions of two kinds of equations. We also obtain results about the uniqueness and the quasi-uniqueness of the Cauchy problems of these equations. A method similar to that of Agmon-Nirenberg is used to study the uniqueness of the Cauchy problem for the non-degenerate linear case.

scholarly journals Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Diblík ◽  
Michal Fečkan ◽  
Michal Pospíšil
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Linear Differential Equations ◽  
Multiple Delays ◽  
Initial Value ◽  
Matrix Polynomials ◽  
The Cauchy Problem ◽  
Nonhomogeneous System ◽  
Linear Differential

Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. Solution of corresponding initial value problem is represented using matrix polynomials.

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