Applications of the smooth integral in the theory of weak solutions of ordinary differential equations

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1. P. Antosik J. Mikusinski R. Sikorski, Theory of distributions, The sequential approach Amsterdam-Warsaw, 1973. (1973) MR0365130
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. (1966) MR0203452
3. P. Antosik, On the modulus of a distribution, Bull. Acad. Polon. Sci. Ser. Sc. Mat. Astr. Phys. 15 (1967), 717-722. (1967) Zbl0173.41703MR0512036
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). (1971) 
5. J. Dugundi A. Granas, Fixed point theory, Warszawa 1982. (1982) 
6. V. Doležal, Dynamics of linear systems, Praha 1964. (1964) MR0169744
7. A. F. Filippov, Differential equations with discontinuous right hand side, (Russian). Moskva 1985. (1985) Zbl0571.34001MR0790682
8. S. Fučík A. Kufner, Nonlinear differential equations, (Czech). Academia, Praha 1978. (1978) 
9. I. M. Gelfand G. J. Shilov, Generalized functions and operations on them, (Russian). Moskva 1958. (1958) 
10. A. Halanay D. Wexler, Qualitative theory of impulse systems, (Russian). Moskva 1971. (1971) 
11. T. H. Hildebrandt, On systems of linear differential Stieltjes-integral equations, Illinois Jour, of Math. 3 (1959), 352-373. (1959) MR0105600
12. I. T. Kiguradze, Some singular boundary value problems for odinary differential equations, (Russian). Izdat. Tbiliskogo universiteta, Tbilisi 1975. (1975) MR0499402
13. M. A. Krasnosielski, Topological methods in the theory of nonlinear integral equations, (Russian). Moskva 1956. (1956) 
14. S. G. Krejn, Functional analysis, Moskva 1972. (1972) Zbl0236.47001
15. J. Kurzweil, Generalized ordinary differential equations and continuous dependence on a parameter, Czechoslovak Math. J. 7 (1959), 418-449. (1959) Zbl0094.05902MR0111875
16. J. Kurzweil, Generalized ordinary differential equations, Ibidem 8 (1958), 360-389. (1958) Zbl0102.07003MR0111878
17. J. Kurzweil, Linear differential equations with distributions as coefficients, Bull. Acad. Polon. Sci. Ser. Math. Astr. et Phys. 7 (1959), 557-560. (1959) Zbl0117.34401MR0111887
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. (1964) MR0173804
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. (1968) MR0223626
20. A. Lasota J. Traple, Nicoletti boundary value problem for systems of linear differential equations with distributional perturbations, Ibidem 15 (1971), 103-108. (1971) MR0369785
21. A. J. Levin, On linear differential equations of the second order, (Russian). Dokl. Ak. Nauk SSSR 153 (1963), 1257-1260. (1963) MR0159060
22. J. Ligeza, On an integral inequality, Prace Naukowe U. Śl. w Katowicach, Prace Mat. 7 (1977), 37-41. (1977) Zbl0368.26004MR0432842
23. J. Ligeza, On distributional solutions of some systems of linear differential equations, Časopis pěst. mat. 102 (1977), 30-36. (1977) Zbl0345.34003MR0460756
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. (1979) Zbl0421.34020MR0594426
25. A. D. Myshkis A. M. Samoilenko, System with impulses at given time moments, (Russian). Mat. sb. 74, 116: 2 (1967), 202-208. (1967) MR0221000
26. R. Pfaff, Gewöhnliche lineare Differentialgleichungen n-ter Ordnung mit Distributionskoeffizienten, Proc. of the Royal Society of Edinburgh. Sect. A 85 (1980), 291-298. (1980) Zbl0424.34011MR0574022
27. R. Pfaff, Generalized systems of linear differential equations, Ibidem 89 A (1981), 1-14. (1981) Zbl0475.34005MR0628123
28. Š. Schwabik M. Tvrdý O. Vejvoda, Differential and integral equations, Academia, Praha 1979. (1979) MR0542283
29. J. Traple, Boundary value problems for linear differential equations with distributional perturbations, Zeszyty Naukowe U. J., Prace Mat. 17 (1975), 119-126. (1975) Zbl0352.34013MR0399552
30. Ch. de la Valleé-Poussin, Sur l'equation differentielle du second ordre, Jour. Math. Pures et Apl. (1929), 125-144. (1929) 
31. N.I. Wasilev J. A. Klokov, Elements of the theory of boundary value problems for ordinary differential equations, (Russian). Riga 1978. (1978) 
32. Š. Schwabik, Generalized differential equations, Rozpravy ČSAV, Praha 1985. (1985) Zbl0594.34002
33. J. Ligeza, Weak solutions of ordinary differential equations, Prace Naukowe U. Śl. w Katowicach Nr 842 (1986). (1986) Zbl0605.34009MR0868863