Necessary Conditions for Multiple Integral Problem in the Calculus of Variations.
New concepts of well-posedness for optimization problems with variational inequality constraints.
New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces.
New system of general nonconvex variational inequalities.
Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics
This paper is devoted to the study of a class of hemivariational inequalities which was introduced by P. D. Panagiotopoulos [31] and later by Z. Naniewicz [22]. These variational formulations are natural nonconvex generalizations [15–17], [22–33] of the well-known variational inequalities. Several existence results are proved in [15]. In this paper, we are concerned with some related results and several applications.
Non-compact random generalized games and random quasi-variational inequalities.
Nonlinear Commutators and Jacobians.
Nonlinear parabolic variational inequalities
Nonlinear retarded integral inequalities with two variables and applications.
Nonlinear Variational Inequalities and Maximal Monotone Mappings in Banach Spaces.
Nonlinear Variational Inequalities Depending on a Parameter
This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.
Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces.
Nonsmooth optimal design problems for the Kirchhoff plate with unilateral conditions
Non-smooth variational bifurcation
We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.
Numerical analysis for optimal shape design in elliptic boundary value problems
Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed...
Numerical analysis of oscillations in nonconvex problems.
Numerical approaches to rate-independent processes and applications in inelasticity
A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...
Numerical approximation of relaxed variational problems.
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical Solution of the Obstacle Problem by the Penalty Method. Part II. Time-Dependent Problem.