Abstract
We establish conditions for the unique existence of a solution of a problem with formal initial conditions. We investigate the problem of its solvability in the case where a solution is not unique.
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V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Operator Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
B. I. Ptashnik, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
V. S. Il’kiv, “Perturbations of a nonlocal problem for differential equations with pseudodifferential coefficients,” Differents. Uravn., 26, No. 11, 1962–1971 (1990).
B. L. van der Waerden, Algebra, Springer, Berlin (1967, 1971).
V. S. Il’kiv, V. N. Polishchuk, B. I. Ptashnik, and B. O. Salyga, “A nonlocal multipoint problem for pseudodifferential operators with analytic symbols,” Ukr. Mat. Zh., 38, No. 5, 582–587 (1976).
V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Calculations [in Russian], Nauka, Moscow (1984).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 877–888, July, 1998.
This work was partially supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.
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Il’kiv, V.S. A problem with formal initial conditions for differential equations with constant pseudodifferential coefficients. Ukr Math J 50, 995–1008 (1998). https://doi.org/10.1007/BF02528829
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DOI: https://doi.org/10.1007/BF02528829