The structure of extremals of a class of second order variational problems
The structure of the critical set in the general mountain pass principle
The sufficient condition for linear constant time-lag systems to be normal systems
The system of generalized set-valued equilibrium problems.
The union of uniform closed balls conjecture
The use of monotone norms in epigraphical analysis.
The use of Young measures for constructing minimizing sequences in the calculus of variations.
The value function representing Hamilton–Jacobi equation with hamiltonian depending on value of solution
In the paper we investigate the regularity of the value function representing Hamilton–Jacobi equation: − Ut + H(t, x, U, − Ux) = 0 with a final condition: U(T,x) = g(x). Hamilton–Jacobi equation, in which the Hamiltonian H depends on the value of solution U, is represented by the value function with more complicated structure than the value function in Bolza problem. This function is described with the use of some class of Mayer problems related to the optimal control theory and the calculus of...
The variational contact problem for elastic objects of different dimensions.
The viscosity subdifferential of the sum of two functions in Banach spaces. I: First order case.
The von Neumann minimax theorem revisited
The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory
We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field with a time-dependent...
Théorème de minimax sans topologie ni convexité
Dans cete note, nous présentons un théorème de minimax (Théorème A) formulé seulement en langage de la théorie des ensembles. Ce résultat permet de déduire de façon immédiate (en utilisant un lemme de topologie générale) plusieurs théorèmes de minimax bien connus.
Theorems on lower semicontinuity and relaxation for integrands with fast growth.
Theoretical analysis and control results for the Fitzhugh-Nagumo equation.
Three-step iterations for mixed quasi variational-like inequalities.
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian-Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. Involving...
Time dependent Dirichlet space, mixed Dirichlet problem and pseudo-differential operators
Time optimal control of a second order nonlinear plant
Time optimal control of the heat equation with pointwise control constraints
Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained....