Abstract
In terms of boundary conditions we establish criteria for maximal dissipativity and maximal accretiveness (in particular, self-adjointness and maximal nonnegativity)for the operators mentioned in the title. We construct the resolvents of these operators.
Similar content being viewed by others
Literature cited
V. I. Gorbachuk and M. L. Gorbachuk,Boundary-Value Problems for Operator-Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
V. I. Gorbachuk, M. L. Gorbachuk, and A. N. Kochubei, “Theory of extensions of symmetric operators and boundary-value problems for differential equations,”Ukr. Mat. Zh.,41, No. 10, 1299–1313 (1989).
T. Kato,Perturbation Theory for Linear Operators, Springer, New York (1966).
A. N. Kochubei, “On the extension of symmetric operators and symmetric binary relations,”Mat. Zamet.,17, No. 1, 41–48 (1975).
A. N. Kochubei, “On the extension of a positive-definite operator,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 3, 168–171 (1979).
V. E. Lyantse, “On some relations between closed operators,”Dokl. Akad. Nauk SSSR,204, No. 3, 542–545 (1972).
O. Ya. Mil'o and O. G. Storozh, “On a class of finite-dimensional perturbations of a positive-definite operator,”Dop. Nats. Akad. Nauk Ukr., No. 11, 39–44 (1996).
V. A. Mikhailets, “Spectra of operators and boundary-value problems,” in:Spectral Analysis of Differential Operators [in Russian], Mathematical Institute of the Academy of Sciences of the Ukrainian SSR, Kiev (1980), pp. 106–131.
S. G. Mikhlin,Mathematical Physics: An Advanced Course, North-Holland, Amsterdam (1970).
M. A. Naimark,Linear Differential Operators, Ungar New York (1967).
G. E. Shilov,Mathematical Analysis: A Special Course, Pergamon, Oxford (1965).
Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 26–31.
Rights and permissions
About this article
Cite this article
Mil'o, O.Y., Storozh, O.G. Sectoriality conditions and solvability of differential boundary operators of sturm-liouville type with multipoint-integral boundary conditions. J Math Sci 96, 2961–2965 (1999). https://doi.org/10.1007/BF02169688
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02169688