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In this paper, we consider hemivariational–variational inequalities driven by uniformly monotone or d -monotone operators in Banach spaces. We establish related minimization principles leading to the existence and uniqueness of solutions to the inequality considered as well as we suggest the Ritz type numerical approximations. The theoretical results obtained are next applied to some problems inspired by models from contact mechanics. [ABSTRACT FROM AUTHOR]

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

We investigate the existence of variational generalized solutions to coercive competitive equations driven by a competing p , q − Laplacian type operator with weigth depending on the gradient. An abstract existence result based on a Galerkin scheme is therefore obtained and subsequently applied. [ABSTRACT FROM AUTHOR]

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush–Kuhn–Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p ( · ) − Laplacian on weighted finite graphs. Several auxiliary inequalities for the discrete p ( · ) − Laplacian on finite graphs are also derived. Positive solutions are considered. [ABSTRACT FROM AUTHOR]

The paper presents the new method of the natural frequencies and damping identification based on the Artificial Intelligence (AI) Particle Swarm Optimization (PSO) algorithm. The identification is performed in the frequency domain. The algorithm performs two PSO-based steps and introduces some modifications in order to achieve quick convergence and low estimation error of the identified parameters’ values for multi-mode systems. The first stage of the algorithm concentrates on the natural frequencies estimation. Using the information about the natural frequencies, measurement data are filtered and corrected dampings as well as amplitudes are calculated for each preliminary identified mode. This allows regrouping particles to the area around proper parameters values. Particle regrouping is based on the physical properties of modally tested structures. This differs the algorithm from other PSO based algorithms with particles regrouping. In the second stage of the algorithm parameters of all modes are tuned together in order to adjust estimates. The procedure of identification, as well as the appropriate algorithm, is presented and some SISO examples are provided. Results are compared with the results obtained for the selected, already developed modal identification methods. The paper presents practical application of AI method for mechanical systems identification. [ABSTRACT FROM AUTHOR]

In the paper a method of optimal spindle speed determination for vibration reduction during ball-end milling of flexible details is proposed. In order to reduce vibration level, an original procedure of the spindle speed optimisation, based on the Liao–Young criterion [ 1 ], is suggested. As the result, an optimal, constant spindle speed value is determined. For this purpose, non-stationary computational model of machining process is defined. As a result of modelling, a hybrid system is described. This model consists of following subsystems, i.e. stationary model of one-side-supported flexible workpiece (modal subsystem), non-stationary discrete model of ball-end mill (structural subsystem) and conventional contact point between tool and workpiece (connective subsystem). The method requires identification of some natural frequencies of stationary modal subsystem. To determine them, appropriate modal experiments have to be performed on the machine tool, just before machining. Examples of vibration surveillance during cutting process on two high speed milling machines Mikron VCP 600 and Alcera Gambin 120CR are illustrated. [ABSTRACT FROM AUTHOR]

An n -th order delayed differential equation y (n) (t) = f (t , y t , y t ′ , ... , y t (n − 1) ) is considered, where y t (θ) = y (t + θ) , θ ∈ [ − τ , 0 ] , τ > 0 , if t → ∞. A criterion is formulated guaranteeing the existence of a solution y = y (t) in a cone 0 < (− 1) i − 1 y (i − 1) (t) < (− 1) i − 1 φ (i − 1) (t) , i = 1 , ... , n where φ is an n -times continuously differentiable function such that 0 < (− 1) i φ (i) (t) , i = 0 , ... , n. The proof is based on a similar result proved first for a system of delayed differential equations equivalent in a sense. Particular linear cases are considered and an open problem is formulated as well. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the continuous dependence on parameters for the mountain pass solutions of second order discrete equations with -Laplacian and Dirichlet type boundary conditions. We show that assumptions leading to the existence of nontrivial solutions lead also to its continuous dependence on parameters. We investigate also the uniqueness of solutions. [Copyright &y& Elsevier]

Abstract: We consider the existence and multiplicity of solutions to discrete boundary value problems with the use of critical point theory combined with some monotonicity argument. We consider both sub- and super-linear problems. [Copyright &y& Elsevier]

Abstract: We derive a dual variational method in order to obtain the existence of a bounded solution to a certain nonlinear system with non-monotone nonlinearities. We consider such a system representing a difference equation arising from evaluating some Dirichlet boundary value problems. [Copyright &y& Elsevier]

Abstract: We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden–Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigating the dependence on parameters of discrete boundary value problems. [Copyright &y& Elsevier]

Abstract: Using a direct variational approach with no global growth conditions on the nonlinear term, we consider the existence of solutions and their dependence on a functional parameter for the fourth order Dirichlet problem connected with the elastic beam equation. We investigate also the existence of an optimal process for such an optimal control problem in which the dynamics is described by the beam equation. [ABSTRACT FROM AUTHOR]

Abstract: We begin with using a dual variational method in proving the existence of solutions to a beam equation with Dirichlet boundary conditions and with a non-monotone nonlinear term. Later we investigate the dependence on a control parameter for the state equation. We find the optimal process for the optimal control problem in which the dynamics is governed by the nonlinear beam equation. [Copyright &y& Elsevier]

Abstract: We consider the existence of solutions and the continuous dependence on a parameter results for fourth-order Dirichlet problem connected with the elastic beam equation. We introduce a dual variational method. [Copyright &y& Elsevier]

Abstract: We study the existence of solutions, their stability and numerical approximations for elliptic Dirichlet problems with some general growth conditions. We consider an abstract family of equations for which we derive a new variational method to obtain existence and stability results which a further applied to concrete problems. Galerkin type approximations are also obtained. [Copyright &y& Elsevier]

Abstract: We undertake the question of the multiplicity of solutions to the discrete Emden–Fowler BVP by correcting some results contained in . [Copyright &y& Elsevier]

• Nash-type equilibria are being investigated via monotonicity methods. • Some interplay between monotonicity and variational methods is shown. • Methods present an improvement over the applications of generalized contractions. Based on the Browder–Minty Theorem we obtain abstract existence results for a system of non–potential equations that we further apply to the existence of the Nash–type equilibrium. Applications to systems of semilinear partial differential equations are given. [ABSTRACT FROM AUTHOR]