For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent [Formula: see text] holds shy set in measure-theoretic sense. This exhibits admit no observable chaos, notion of which was formulated by L.S. Young. We further such phenomenon chaos is robust under text]-perturbation systems.

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequality. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutio...

In this paper we derive necessary optimality conditions involving Mordukhovich coderivatives for optimal control problems of strongly monotone variational inequalities.

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments.

Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.