Linear distributional differential equations of the second order

Milan Tvrdý

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 4, page 415-436
  • ISSN: 0862-7959

Abstract

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The paper deals with the linear differential equation (0.1) ( p u ' ) ' + q ' u = f ' ' with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).

How to cite

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Tvrdý, Milan. "Linear distributional differential equations of the second order." Mathematica Bohemica 119.4 (1994): 415-436. <http://eudml.org/doc/29274>.

@article{Tvrdý1994,
abstract = {The paper deals with the linear differential equation (0.1) $(pu^\{\prime \})^\{\prime \}+q^\{\prime \}u=f^\{\prime \prime \}$ with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).},
author = {Tvrdý, Milan},
journal = {Mathematica Bohemica},
keywords = {regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; boundary value problem; numerical approximation; uniqueness; distribution; regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; uniqueness; boundary value problem; numerical approximation},
language = {eng},
number = {4},
pages = {415-436},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear distributional differential equations of the second order},
url = {http://eudml.org/doc/29274},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Tvrdý, Milan
TI - Linear distributional differential equations of the second order
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 4
SP - 415
EP - 436
AB - The paper deals with the linear differential equation (0.1) $(pu^{\prime })^{\prime }+q^{\prime }u=f^{\prime \prime }$ with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).
LA - eng
KW - regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; boundary value problem; numerical approximation; uniqueness; distribution; regulated functions; Perron-Stieltjes integral; Kurzweil integral; generalized differential equation; linear second order equation; distributional coefficients; existence; uniqueness; boundary value problem; numerical approximation
UR - http://eudml.org/doc/29274
ER -

References

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  10. Ligęza J., Product of measures and regulated functions, Generalized Functions and Convergence (Memorial Volume for Professor Jan Mikusiński, 13-18 June 1988) (Piotr Antosik and Andrzej Kamiński Katowice, eds.). World Scientific, Praha, Singapore-New Jersey-London-Hong Kong, 1988, pp. 175-179. (1988) MR1085505
  11. Mingarelli A.B., Volterra-Stieltjes Integral Equations and Generalized Ordinary Differential Expressions, Lecture Notes in Mathematics, 989, Springer-Verlag, Berlin-Heidelberg-New York, 1983. (1983) Zbl0516.45012MR0706255
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  20. Schwabik Š., Generalized Ordinary Differential Equations, World Scientific, Singapore, 1992. (1992) Zbl0781.34003MR1200241
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  24. Zavalishchin S.G., Sesekin A.N., Impulse Processes, Models and Applications, Nauka, Moscow, 1991. (In Russian.) (1991) MR1126685

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