Generalized solutions of ordinary linear differential equations in the Colombeau algebra

Jan Ligęza

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 2, page 123-146
  • ISSN: 0862-7959

Abstract

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In this paper first order systems of linear of ODEs are considered. It is shown that these systems admit unique solutions in the Colombeau algebra ( 𝐑 1 ) .

How to cite

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Ligęza, Jan. "Generalized solutions of ordinary linear differential equations in the Colombeau algebra." Mathematica Bohemica 118.2 (1993): 123-146. <http://eudml.org/doc/29208>.

@article{Ligęza1993,
abstract = {In this paper first order systems of linear of ODEs are considered. It is shown that these systems admit unique solutions in the Colombeau algebra $\mathcal \{L\}(\mathbf \{R\}^1)$.},
author = {Ligęza, Jan},
journal = {Mathematica Bohemica},
keywords = {linear Cauchy problem; Colombeau algebra of generalized distributions; existence; uniqueness; generalized ordinary differential equation; Cauchy problem generalized function; distribution; linear Cauchy problem; Colombeau algebra of generalized distributions; existence; uniqueness},
language = {eng},
number = {2},
pages = {123-146},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized solutions of ordinary linear differential equations in the Colombeau algebra},
url = {http://eudml.org/doc/29208},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Ligęza, Jan
TI - Generalized solutions of ordinary linear differential equations in the Colombeau algebra
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 2
SP - 123
EP - 146
AB - In this paper first order systems of linear of ODEs are considered. It is shown that these systems admit unique solutions in the Colombeau algebra $\mathcal {L}(\mathbf {R}^1)$.
LA - eng
KW - linear Cauchy problem; Colombeau algebra of generalized distributions; existence; uniqueness; generalized ordinary differential equation; Cauchy problem generalized function; distribution; linear Cauchy problem; Colombeau algebra of generalized distributions; existence; uniqueness
UR - http://eudml.org/doc/29208
ER -

References

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  12. A. Lasota J. Traple, Nicoletti boundary value problem for system of linear differential equations with distributional perturbations, Prace Mathematyczne Uniwersytetu Jagiellonskiego, Kraków 15(1971), 103-108. (1971) MR0369785
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  15. J. Persson, The Cauchy problem for linear distribution differential equations, Funkcial. Ekvac. 30 (1987), 163-168. (1987) Zbl0643.34004MR0915270
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  17. Š. Schwabik M. Tvrdý O. Vejvoda, Differential and Integral Equations, Praha, 1979. (1979) MR0542283
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