Existence and comparison principles for general quasilinear variational–hemivariational inequalities

AbstractWe consider quasilinear elliptic variational–hemivariational inequalities involving convex, lower semicontinuous and locally Lipschitz functionals. We provide a generalization of the fundamental notion of sub- and supersolutions on the basis of which we then develop the sub–supersolution method for variational–hemivariational inequalities, including existence, comparison, compactness and extremality results

Quasilinear elliptic inclusions of hemivariational type: Extremality and compactness of the solution set

AbstractWe consider the Dirichlet boundary value problem for an elliptic inclusion governed by a quasilinear elliptic operator of Leray–Lions type and a multivalued term which is given by the difference of Clarke's generalized gradient of some locally Lipschitz function and the subdifferential of some convex function. Problems of this kind arise, e.g., in mechanical models described by nonconvex and nonsmooth energy functionals that result from nonmonotone, multivalued constitutive laws. Our main goal is to characterize the solution set of the problem under consideration. In particular we are going to prove that the solution set possesses extremal elements with respect to the underlying natural partial ordering of functions, and that the solution set is compact. The main tools used in the proofs are abstract results on pseudomonotone operators, truncation, and special test function techniques, Zorn's lemma as well as tools from nonsmooth analysis

Nonhomogeneous degenerate quasilinear problems with convection

The aim of the paper is to study a Dirichlet problem whose equation is driven by a degenerate p-Laplacian with a weight depending on the solution and whose reaction is a convection term, thus depending on the solution and its gradient. The existence of a weak solution is proven by arguing through a truncated auxiliary problem. A major part of the proof consists in showing that the solutions are bounded. (c) 2022 Elsevier Ltd. All rights reserved

DIRICHLET PROBLEMS WITH ANISOTROPIC PRINCIPAL PART INVOLVING UNBOUNDED COEFFICIENTS

This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates

Quasilinear dirichlet problems with degenerated p-laplacian and convection term

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions

A sub-supersolution approach for robin boundary value problems with full gradient dependence

The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A subsupersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions

Разработка системы удержания персонала предприятия по производству электрооборудования

Объектом исследования являются причины текучести персонала на предприятии и методы их устранения. Цель работы – разработка системы удержания сотрудников на предприятии. В процессе исследования проводился анализ системы удержания персонала на предприятии АО «Узэлектроаппарат».Object of research are the reasons for staff turnover at the company and ways to address them . Purpose - to develop a system of retention of employees in the enterprise. The study analyzed personnel retention system at the enterprise JSC " Uzelektroapparat

Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray-Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis