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References
B.Fisher, The product of distributions, Quart. J. Math. Oxford (2) 22 (1971), 291–298.
O.Hájek, Book review, Bull. Amer. Math. Soc. 12 (1985), 272–279.
Kurzweil, Generalized ordinary differential equations, Czechoslovak Math. J. 8 (1958), 360–388.
J.Ligęza, Weak solutions of ordinary differential equations, Prace Nauk. Univ. Śląsk. Katowic. 842 (1986).
J.Lersson, Second order linear differential equations with measures as coefficients, Mathematiche 36 (1981), 151–171.
J.Persson, Generalized nonlinear ordinary differential equations linear in measures, Ann. Mat. Pura Appl. (4) 32 (1982), 177–187.
J.Persson, The wave equation with measures as potentials and related topics, Rend. Sem. Mat. Univ. Politec. Torino. Fascicolo Speciale settembre (1983), 207–219.
J.Persson, Linear distribution differential equations, Comment. Math. Univ. St. Paul. 33 (1984), 119–126.
J.Persson, The vibrating rod, Boll. Un. Mat. Ital. (7) 1-B (1987), 185–195.
J.Persson, The Cauchy problem for linear distribution differential equations, Funkcial. Ekvac. 30 (1987), 163–168.
J.Persson, Wave equations with measures as coefficients, in “Hyperbolic equations, Proceedings of the conference on Hyperbolic Equations and related topics, University of Padova, 1985”, ed. F. Colombini and M. K. V. Murthy. Harlow: Longman 1987, pp. 130–140.
J.Persson, Fundamental theorems for linear measure differential equations, Math. Scand. 62 (1988), 19–43.
J.Persson, Invariance of the Cauchy problem for distribution differential equations, in “Generalized functions, convergence structures, and their applications”, (ed.) B. Stankovic, E. Pap, S. Pilipovic and V. S. Vladimirov. New York und London: Plenum 1988, pp. 279–284.
J.Persson, The regularization problem for the wave equation with measures as potentials and driving forces, in “Recent developments in hyperbolic equations Proceeedings of the conference on hypeerbolic equations, University of Pisa, 1987”, (ed.) L. Cattabriga, F. Colombini, S. Spagnolo. Harlow: Longman 1988, pp. 265–289.
J.Persson, Distribution differential equations. Regularization and bending of a rod, Math. Scand. 66 (1990), 291–300.
J.Persson, Regularization of non-linear measure differential equations, Matematiche 44 (1989), 113–130.
R.Pfaff, Gewöhnliche lineare Differentialgleichungen zweiter Ordnung mit Distributions-koeffizienten, Arch. Math. (Basel) 32 (1979), 469–478.
R.Pfaff, Gewöhnliche lineare Differentialgleichungen n-ter Ordnung mit Distributions-koeffizienten, Proc. Roy. Soc. Edinburgh, Sect. A, 85-A (1980), 291–298.
R.Paff, Generalized systems of linear differential equations, Proc. Roy. Soc. Edinburgh, Sect. A, 89-A (1981), 1–14.
A. N.Sesekin, Nonlinear differential equations containing products of discontinuous and generalized functions (Russian), in “Generalized functions and differential equations”, ed. V. K. Ivanov and Yu. Amatov, Akad. Nauk SSSR, Ural. Nauchn. Tsentr, Sverdlovsk 1985, pp. 48–61, 103. pp. 48–61, 103.
A. N.Sesekin, Discontinuous solutions of integral equations and their estimates (Russian), in “Generalized functions and their estimates,ed. V. K. Ivanov and Yu. Amatov. Akad. Nauk SSSR, Ural. Nauch. Tsentr, Sverdlovsk 1985, pp.62–68.
Š.Šchwabik, M.Tvrdý, O.Vejvoda, “Differential and integral equations. Boundary values and adjoints”, Dordrecht: Reidel 1979.
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Persson, J. Regularization of a non-linear wave equation with measures as potential and driving force. Ann Glob Anal Geom 9, 145–159 (1991). https://doi.org/10.1007/BF00776853
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DOI: https://doi.org/10.1007/BF00776853