| Title:
|
Applications of the smooth integral in the theory of weak solutions of ordinary differential equations (English) |
| Title:
|
Aplikace hladkého integrálu v teorii slabých řešení obyčejných diferenciálních rovnic (Czech) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Časopis pro pěstování matematiky |
| ISSN:
|
0528-2195 |
| Volume:
|
114 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
113-132 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 0686.34021 |
| idMR:
|
MR1063756 |
| DOI:
|
10.21136/CPM.1989.108710 |
| . |
| Date available:
|
2009-09-23T09:51:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108710 |
| . |
| Reference:
|
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| Reference:
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[2] P. Antosik: Order with respect to a measure and its application to the investigation of the product of generalized functions.(Russian). Studia Math. 26 (1966), 247-262. MR 0203452 |
| Reference:
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[3] P. Antosik: On the modulus of a distribution.Bull. Acad. Polon. Sci. Ser. Sc. Mat. Astr. Phys. 15 (1967), 717-722. Zbl 0173.41703, MR 0512036 |
| Reference:
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[4] T. Dlotko: Application of the notation of rotation of a vector field in the theory of differential equations and their generalizations.(Polish). Prace Naukowe U. Śl. w Katowicach 32 (1971). |
| Reference:
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[5] J. Dugundi A. Granas: Fixed point theory.Warszawa 1982. |
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[6] V. Doležal: Dynamics of linear systems.Praha 1964. MR 0169744 |
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[7] A. F. Filippov: Differential equations with discontinuous right hand side.(Russian). Moskva 1985. Zbl 0571.34001, MR 0790682 |
| Reference:
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[8] S. Fučík A. Kufner: Nonlinear differential equations.(Czech). Academia, Praha 1978. |
| Reference:
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[9] I. M. Gelfand G. J. Shilov: Generalized functions and operations on them.(Russian). Moskva 1958. |
| Reference:
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[10] A. Halanay D. Wexler: Qualitative theory of impulse systems.(Russian). Moskva 1971. |
| Reference:
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[11] T. H. Hildebrandt: On systems of linear differential Stieltjes-integral equations.Illinois Jour, of Math. 3 (1959), 352-373. MR 0105600 |
| Reference:
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[12] I. T. Kiguradze: Some singular boundary value problems for odinary differential equations.(Russian). Izdat. Tbiliskogo universiteta, Tbilisi 1975. MR 0499402 |
| Reference:
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[13] M. A. Krasnosielski: Topological methods in the theory of nonlinear integral equations.(Russian). Moskva 1956. |
| Reference:
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[14] S. G. Krejn: Functional analysis.Moskva 1972. Zbl 0236.47001 |
| Reference:
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[15] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J. 7 (1959), 418-449. Zbl 0094.05902, MR 0111875 |
| Reference:
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[16] J. Kurzweil: Generalized ordinary differential equations.Ibidem 8 (1958), 360-389. Zbl 0102.07003, MR 0111878 |
| Reference:
|
[17] J. Kurzweil: Linear differential equations with distributions as coefficients.Bull. Acad. Polon. Sci. Ser. Math. Astr. et Phys. 7 (1959), 557-560. Zbl 0117.34401, MR 0111887 |
| Reference:
|
[18] A. Lasota Z. Opial: L'existence et l'unicité des solutions du problème d'interpolations pour l'equation differentielle ordinaire d'ordre n.Ann. Polon. Math. 15 (1964), 254-271. MR 0173804 |
| Reference:
|
[19] A. Lasota F. H. Szafraniec: Application of differential equations with distributional coefficients to optimal control theory.Zeszyty Naukowe U. J., Prace Mat. 12 (1968), 31 - 37. MR 0223626 |
| Reference:
|
[20] A. Lasota J. Traple: Nicoletti boundary value problem for systems of linear differential equations with distributional perturbations.Ibidem 15 (1971), 103-108. MR 0369785 |
| Reference:
|
[21] A. J. Levin: On linear differential equations of the second order.(Russian). Dokl. Ak. Nauk SSSR 153 (1963), 1257-1260. MR 0159060 |
| Reference:
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[22] J. Ligeza: On an integral inequality.Prace Naukowe U. Śl. w Katowicach, Prace Mat. 7 (1977), 37-41. Zbl 0368.26004, MR 0432842 |
| Reference:
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[23] J. Ligeza: On distributional solutions of some systems of linear differential equations.Časopis pěst. mat. 102 (1977), 30-36. Zbl 0345.34003, MR 0460756 |
| Reference:
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[24] J. Ligeza: On generalized solutions of boundary value problems for non linear differential equations of second order.Prace Naukowe U. Śl. w Katowicach, Prace Mat. 9 (1979), 20-29. Zbl 0421.34020, MR 0594426 |
| Reference:
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[25] A. D. Myshkis A. M. Samoilenko: System with impulses at given time moments.(Russian). Mat. sb. 74, 116: 2 (1967), 202-208. MR 0221000 |
| Reference:
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[26] R. Pfaff: Gewöhnliche lineare Differentialgleichungen n-ter Ordnung mit Distributionskoeffizienten.Proc. of the Royal Society of Edinburgh. Sect. A 85 (1980), 291-298. Zbl 0424.34011, MR 0574022 |
| Reference:
|
[27] R. Pfaff: Generalized systems of linear differential equations.Ibidem 89 A (1981), 1-14. Zbl 0475.34005, MR 0628123 |
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[28] Š. Schwabik M. Tvrdý O. Vejvoda: Differential and integral equations.Academia, Praha 1979. MR 0542283 |
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[29] J. Traple: Boundary value problems for linear differential equations with distributional perturbations.Zeszyty Naukowe U. J., Prace Mat. 17 (1975), 119-126. Zbl 0352.34013, MR 0399552 |
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[30] Ch. de la Valleé-Poussin: Sur l'equation differentielle du second ordre.Jour. Math. Pures et Apl. (1929), 125-144. |
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[31] N.I. Wasilev J. A. Klokov: Elements of the theory of boundary value problems for ordinary differential equations.(Russian). Riga 1978. |
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[32] Š. Schwabik: Generalized differential equations.Rozpravy ČSAV, Praha 1985. Zbl 0594.34002 |
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|
[33] J. Ligeza: Weak solutions of ordinary differential equations.Prace Naukowe U. Śl. w Katowicach Nr 842 (1986). Zbl 0605.34009, MR 0868863 |
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