The variational stability of an optimal control problem for Volterra-type equations

We study the variational stability of an optimal control problem for a Volterra-type nonlinear functional-operator equation. This means that for this optimal control problem (P _? ) with a parameter ? we study how its minimum value min(P _? ) and its set of minimizers argmin(P _? ) depend on ?. We illustrate the use of the variational stability theorem with a series of particular problems.     

Lp-Continuous extreme selectors of multifunctions with decomposable values: Relaxation theorems

Some density theorems of L _p-continuous selectors whose values are extreme points are proved for a class of multivalued maps. applications to the Darboux problem for a differential inclusion are presented.Supported in part by RFFI Grant 93-011-264.     

Steady-state solutions of the Vlasov-Maxwell system and their stability

The study of the Vlasov-Maxwell system is reduced to nonlinear elliptic equations in the stationary case and hyperbolic equations in the nonstationary case. On this basis, theorems on the existence of solutions and sufficient conditions of Lyapunov stability are obtained. The cases are considered when electromagnetic fields and distribution functions can be constructed in an implicit form.     

Consideration of the field of the crystal-chemical environment in the cluster-cell method for evaluating the cation distribution in crystals with a spinel structure

Volgograd Polytechnical Institute. Institute of Metallurgy, Academy of Sciences of the USSR, Ural Branch. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 2, pp. 146–148, March–April, 1991.     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

A Multivalued History-Dependent Operator and Implicit Evolution Inclusions. II

Siberian Mathematical Journal - Continuing the first part of this work, we study an implicit evolution inclusion with time-dependent maximal monotone operator in a separable...