Abstract
For an elliptic second-order differential equation in a Banach space, we give a description of all solutions of the homogeneous Dirichlet and Neumann problems and establish conditions under which these problems are uniquely solvable.
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References
S. G. Krein,Linear Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1967).
H. Komatsu, “Fractional powers of operators,”Pacif. J. Math.,19, No. 2, 285–346 (1966).
A. V. Knyazyuk,Boundary Values of the Solutions of Evolutionary Equations in Banach Spaces [in Russian], Author's Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1985).
V. M. Gorbachuk and A. V. Knyazyuk, “Limiting values of solutions of operator-differential equations,”Usp. Mat. Nauk,44, No. 3, 55–91 (1989).
A. Balakrischnan, “Fractional powers of closed operators and the semigroups generated by them,”Pacif. J. Math.,10, No. 2, 419–439 (1960).
A. V. Knyazyuk, “Uniqueness in the Dirichlet problem on a semiaxis in a Banach space,” in:Nonlinear Problems in Mathematical Physics [in Russian], Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk (1987).
V. M. Gorbachuk, “Behavior of solutions of a first-order differential equation in a Banach space at infinity,”Ukr. Mat. Zh.,40, No. 5, 629–632 (1988).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1564–1567, November, 1994.
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Gorbachuk, V.M. On the uniqueness of solutions of the Dirichlet and Neumann problems for an elliptic second-order differential equation on a semiaxis. Ukr Math J 46, 1730–1734 (1994). https://doi.org/10.1007/BF01058891
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DOI: https://doi.org/10.1007/BF01058891