A new method for solving monotone generalized variational inequalities.
A new method for the obtaining of eigenvalues of variational inequalities of the special type (Preliminary communication)
A new method of proof of Filippov’s theorem based on the viability theorem
Filippov’s theorem implies that, given an absolutely continuous function y: [t 0; T] → ℝd and a set-valued map F(t, x) measurable in t and l(t)-Lipschitz in x, for any initial condition x 0, there exists a solution x(·) to the differential inclusion x′(t) ∈ F(t, x(t)) starting from x 0 at the time t 0 and satisfying the estimation where the function γ(·) is the estimation of dist(y′(t), F(t, y(t))) ≤ γ(t). Setting P(t) = x ∈ ℝn: |x −y(t)| ≤ r(t), we may formulate the conclusion in Filippov’s theorem...
A new minimal point theorem in product spaces.
A new projection algorithm for generalized variational inequality.
A new proof of the Riemann-Poincaré uniformization theorem.
A new subdifferential in quasiconvex analysis.
A new system of generalized nonlinear relaxed cocoercive variational inequalities.
A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces.
A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
A nonlinear plate control without linearization
In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as...
A nonlocal singular perturbation problem with periodic well potential
For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a -convergence theorem and show compactness up to translation in all and the optimal Orlicz space for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher (1994) for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.
A nonlocal singular perturbation problem with periodic well potential
For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all Lp and the optimal Orlicz space for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher (1994) for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.
A nontrivial solution for Neumann noncoercive hemivariational inequalities
In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.
A note on a class of equilibrium problems with equilibrium constraints
The paper concerns a two-level hierarchical game, where the players on each level behave noncooperatively. In this way one can model eg an oligopolistic market with several large and several small firms. We derive two types of necessary conditions for a solution of this game and discuss briefly the possibilities of its computation.
A note on approximate solutions in parametric semi-infinite optimization
A note on Banach spaces and sub differentials of convex functions
A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower...
A note on convergence of level sets.
A note on equality of functional envelopes
We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in , , then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.