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We introduce a type of mixed variational inequality driven by a uniformly monotone operator for which we investigate the existence and uniqueness problem by applying techniques suggested in [12]. We apply the abstract results obtained to a mixed boundary value problems inspired by contact mechanics but with the elasticity operator being not necessarily strongly monotone. We allow this operator to be a uniformly monotone acting from a reflexive Banach space into its dual. [ABSTRACT FROM AUTHOR]

Modern industry expectations in terms of milling operations often demand the milling of the flexible details by using slender ball-end tools. This is a difficult task because of possible vibration occurrence. Due to existence of certain conditions (small depths of cutting, regeneration phenomena), cutting process may become unstable and self-excited chatter vibration may appear. Frequency of the chatter vibration is close to dominant natural frequency of the workpiece or the tool. One of the methods of chatter vibration avoidance is matching the spindle speed to the optimum phase shift between subsequent cutting edges passes (i.e. the Liao-Young condition). However, the set of optimum spindle speeds from the point of view of vibration reduction may be not optimum one from other points of view. For example milling efficiency or machine tool capabilities cannot be assured. This article presents the idea of a workpiece holder with adjustable stiffness and discusses a new variant of its realization. In the holder, milling process is performed at constant spindle speed and feed speed. In order to avoid vibration the holder stiffness is modified. Stiffness changes modify natural frequencies of the workpiece and thus it is possible to modify dynamic properties of the workpiece in such a way that arbitrary chosen, constant spindle speed will be optimum, due to the Liao-Young condition performance. Calculation of the optimum stiffness is performed before milling, based on the workpieces modal identification results and the finite element model simulations.

In this paper, we study the existence of a Nash‐type equilibrium for a non‐potential nonlinear system by combining variational methods with the monotonicity approach. The advance over existing research is that we can consider systems of Dirichlet problems in which the operator is not necessarily linear. [ABSTRACT FROM AUTHOR]

A method of resolving invexity in mathematical programming problems and developing optimized conditions therefrom is presented.

We provide parameter‐dependent version of the Browder–Minty Theorem in case when the solution is unique utilizing different types of monotonicity and compactness assumptions related to condition (S)2. Potential equations and the convergence of their Euler action functionals are also investigated. Applications towards the dependence on parameters for both potential and nonpotenial nonlinear Dirichlet boundary problems are given. [ABSTRACT FROM AUTHOR]

In this note we are concerned with the proposal of case study approach in teaching mathematical analysis. By describing a simple student's project about the solvability of (nonlinear) equations we aim at indicating that many possible further directions are also possible. [ABSTRACT FROM AUTHOR]