Applications of the smooth integral in the theory of weak solutions of ordinary differential equations
Časopis pro pěstování matematiky, Tome 114 (1989) no. 2, pp. 113-132

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DOI : 10.21136/CPM.1989.108710
Classification : 34B15
Ligęza, Jan. Applications of the smooth integral in the theory of weak solutions of ordinary differential equations. Časopis pro pěstování matematiky, Tome 114 (1989) no. 2, pp. 113-132. doi: 10.21136/CPM.1989.108710
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[1] P. Antosik J. Mikusinski R. Sikorski: Theory of distributions. The sequential approach Amsterdam-Warsaw, 1973. | MR

[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

[3] P. Antosik: On the modulus of a distribution. Bull. Acad. Polon. Sci. Ser. Sc. Mat. Astr. Phys. 15 (1967), 717-722. | MR | Zbl

[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).

[5] J. Dugundi A. Granas: Fixed point theory. Warszawa 1982.

[6] V. Doležal: Dynamics of linear systems. Praha 1964. | MR

[7] A. F. Filippov: Differential equations with discontinuous right hand side. (Russian). Moskva 1985. | MR | Zbl

[8] S. Fučík A. Kufner: Nonlinear differential equations. (Czech). Academia, Praha 1978.

[9] I. M. Gelfand G. J. Shilov: Generalized functions and operations on them. (Russian). Moskva 1958.

[10] A. Halanay D. Wexler: Qualitative theory of impulse systems. (Russian). Moskva 1971.

[11] T. H. Hildebrandt: On systems of linear differential Stieltjes-integral equations. Illinois Jour, of Math. 3 (1959), 352-373. | MR

[12] I. T. Kiguradze: Some singular boundary value problems for odinary differential equations. (Russian). Izdat. Tbiliskogo universiteta, Tbilisi 1975. | MR

[13] M. A. Krasnosielski: Topological methods in the theory of nonlinear integral equations. (Russian). Moskva 1956.

[14] S. G. Krejn: Functional analysis. Moskva 1972. | Zbl

[15] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (1959), 418-449. | MR | Zbl

[16] J. Kurzweil: Generalized ordinary differential equations. Ibidem 8 (1958), 360-389. | MR | Zbl

[17] J. Kurzweil: Linear differential equations with distributions as coefficients. Bull. Acad. Polon. Sci. Ser. Math. Astr. et Phys. 7 (1959), 557-560. | MR | Zbl

[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

[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

[20] A. Lasota J. Traple: Nicoletti boundary value problem for systems of linear differential equations with distributional perturbations. Ibidem 15 (1971), 103-108. | MR

[21] A. J. Levin: On linear differential equations of the second order. (Russian). Dokl. Ak. Nauk SSSR 153 (1963), 1257-1260. | MR

[22] J. Ligeza: On an integral inequality. Prace Naukowe U. Śl. w Katowicach, Prace Mat. 7 (1977), 37-41. | MR | Zbl

[23] J. Ligeza: On distributional solutions of some systems of linear differential equations. Časopis pěst. mat. 102 (1977), 30-36. | MR | Zbl

[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. | MR | Zbl

[25] A. D. Myshkis A. M. Samoilenko: System with impulses at given time moments. (Russian). Mat. sb. 74, 116: 2 (1967), 202-208. | MR

[26] R. Pfaff: Gewöhnliche lineare Differentialgleichungen n-ter Ordnung mit Distributionskoeffizienten. Proc. of the Royal Society of Edinburgh. Sect. A 85 (1980), 291-298. | MR | Zbl

[27] R. Pfaff: Generalized systems of linear differential equations. Ibidem 89 A (1981), 1-14. | MR | Zbl

[28] Š. Schwabik M. Tvrdý O. Vejvoda: Differential and integral equations. Academia, Praha 1979. | MR

[29] J. Traple: Boundary value problems for linear differential equations with distributional perturbations. Zeszyty Naukowe U. J., Prace Mat. 17 (1975), 119-126. | MR | Zbl

[30] Ch. de la Valleé-Poussin: Sur l'equation differentielle du second ordre. Jour. Math. Pures et Apl. (1929), 125-144.

[31] N.I. Wasilev J. A. Klokov: Elements of the theory of boundary value problems for ordinary differential equations. (Russian). Riga 1978.

[32] Š. Schwabik: Generalized differential equations. Rozpravy ČSAV, Praha 1985. | Zbl

[33] J. Ligeza: Weak solutions of ordinary differential equations. Prace Naukowe U. Śl. w Katowicach Nr 842 (1986). | MR | Zbl

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