Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient

AbstractIn this paper we consider an initial boundary value problem for a parabolic inclusion whose multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz function, and whose elliptic operator may be a general quasilinear operator of Leray–Lions type. Recently, extremality results have been obtained in case that the governing multivalued term is of special structure such as, multifunctions given by the usual subdifferential of convex functions or subgradients of so-called dc-functions. The main goal of this paper is to prove the existence of extremal solutions within a sector of appropriately defined upper and lower solutions for quasilinear parabolic inclusions with general Clarke's gradient. The main tools used in the proof are abstract results on nonlinear evolution equations, regularization, comparison, truncation, and special test function techniques as well as tools from nonsmooth analysis

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

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

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

Critical points for nondifferentiable functions in presence of splitting

AbstractA classical critical point theorem in presence of splitting established by Brézis–Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational–hemivariational eigenvalue problems

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

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

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