This is a preview of subscription content, log in via an institution to check access.
Literature Cited
A. A. Lyapunov, “On completely additive vector functions,” Izv. Akad. Nauk. SSSR, Ser. Mat.,4, 465–478 (1940).
J.-L. Lions, Control of Singular Distributed Systems [Russian translation], Nauka, Moscow (1987).
N. Dunford and J. Schwartz, Linear Operators. Part 1: General Theory, Interscience, New York (1958).
H. Schaefer, Topological Vector Spaces, MacMillan, New York (1966).
P. Halmos, “The range of a vector measure,” Bull. Am. Math. Soc.,54, 416–421 (1948).
F. Kingman and A. Robertson, “On a theorem of Lyapunov,” J. London Math. Soc.,43, No. 1, 347–351 (1968).
R. Bartle, N. Dunford, and J. Schwartz, “Weak compactness and vector measures,” Can. J. Math.,7, 289–305 (1955).
J. Schmets, “Sur une generalisation d'une theorem de lyapunov,” Bull. Soc. R. Liege,35, 185–194 (1966).
J. Uhl, “The range of a vector-valued measure,” Proc. Am. Math. Soc.,23, No. 1, 158–163 (1969).
A. S. Matveev, “On the abstract theory of optimal control of systems with distributed parameters,” Sib. Mat. Zh.,29, No. 1, 94–107 (1988).
I. Ekeland and I. Teman, Convex Analysis and Variational Problems [Russian translation], Mir, Moscow, (1979).
V. A. Solonnikov, “On general boundary-value problems for systems that are elliptic in the sense of Douglis-Nirenberg,” Tr. Mat. Inst. im. V. A. Steklova Akad. Nauk SSSR,92, 233–297 (1966).
O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representation of Functions and Imbedding Theorems [in Russian], Nauka, Moscow (1976).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 6, pp. 127–141, November–December, 1990.
Rights and permissions
About this article
Cite this article
Matveev, A.S. Variational analysis in problems on optimization of systems with distributed parameters and vector functions of sets. Sib Math J 31, 984–998 (1990). https://doi.org/10.1007/BF00970064
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970064