Abstract
Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
V. M. Savchin, Mathematical Methods of the Mechanics of Infinite-Dimensional Nonpotential Systems [in Russian], Izdat. UDN, Moscow, 1991.
M. M. Vainberg, The Variational Method and the Method of Monotone Operators [in Russian], Nauka, Moscow, 1972.
V. M. Filippov, V. M. Savchin, and S. G. Shorokhov, “Variational principles for nonpotential operators,” in: Current Problems in Mathematics: Fundamental Directions [in Russian] vol. 40, Itogi Nauki i Tekhniki, VINITI, Moscow, 1992.
V. Volterra, Leçons sur les fonctions de lignes, Gautier-Villars, Paris, 1913.
O. A. Ladyzhenskaya, Mathematical Questions of the Dynamics of a Viscous Incompressible Liquid, Nauka, Moscow, 1970.
Author information
Authors and Affiliations
Additional information
__________
Translated from Matematicheskie Zametki, vol. 80, no. 1, 2006, pp. 87–94.
Original Russian Text Copyright © 2006 by V. M. Savchin, S. A. Budochkina.
Rights and permissions
About this article
Cite this article
Savchin, V.M., Budochkina, S.A. On the existence of a variational principle for an operator equation with second derivative with respect to “ time”. Math Notes 80, 83–90 (2006). https://doi.org/10.1007/s11006-006-0111-x
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11006-006-0111-x