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Generalized-function solutions of differential and functional differential equations. (English) Zbl 0489.34080


MSC:

34K25 Asymptotic theory of functional-differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
46F10 Operations with distributions and generalized functions

Citations:

Zbl 0424.34006
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References:

[1] Aliev, F.S, On the solutions of certain systems of ordinary differential equations in the space of generalized functions, Vestnik moscov. GoS. univ. ser. mat. meh., 5, 3-10, (1973) · Zbl 0266.34069
[2] Wiener, J, Generalized-function solutions of ordinary differential equations, (), 51, abstracts
[3] Wiener, J, Solutions of linear systems in generalized functions, Differencial’nye uravnenija, 6, 1128-1130, (1975)
[4] Wiener, J, A retarded type system with infinitely differentiable coefficients has solutions in generalized functions, Uspehi mat. nauk, 31, 5, 227, (1976)
[5] Wiener, J, Existence of solutions of differential equations with deviating argument in the space of generalized functions, Sibirsk. mat. Z., 6, 1403-1405, (1976)
[6] Wiener, J, Generalized-function solutions of differential equations with a countable number of argument deviations, Differencial’nye uravnenija, 2, 355-358, (1978)
[7] Gel’fand, I.M; Shilov, G.E, Generalized functions, () · Zbl 0159.18301
[8] Mityagin, B.S, Dokl. akad. nauk SSSR, 138, 2, (1961)
[9] Kamke, E, Gew√∂hnliche differentialgleichungen, (1959), Leipzig · Zbl 0194.39301
[10] Zemanian, A.H, Generalized integral transformations, (1969), Interscience New York · Zbl 0181.12701
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