Zdzisław Denkowski

An Introduction to Nonlinear Analysis: Theory

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors. The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.

Optimal Shape Design Problems for a Class of Systems Described by Hemivariational Inequalities

Optimal shape design problems for systems governed by an elliptic hemivariational inequality are considered. A general existence result for this problem is established by the mapping method.

Nontrivial Solutions for Resonant Hemivariational Inequalities

We study a resonant semilinear elliptic hemivariational inequality. Under some assumptions of strong resonance on the Clarke subdifferential of the superpotential, and using nonsmooth critical point theory, the existence of a nontrivial solution of the problem is shown.

Optimal Shape Design for Elliptic Hemivariational Inequalities in Nonlinear Elasticity

Optimal shape design problem for systems governed by elliptic hemivariational inequality which comes from nonlinear elasticity is considered. A general existence result for this problem is established by the mapping method.

Existence of Solutions to Evolution Second Order Hemivariational Inequalities with Multivalued Damping

In this paper we examine an evolution problem which describes the dynamic contact of a viscoelastic body and a foundation. The contact is modeled by a general normal compliance condition and a friction law which are nonmonotone, possibly multivalued and of the subdifferential form while the damping operator is assumed to be coercive and pseudomonotone. We derive a formulation of the model in the form of a multidimensional hemivariational inequality. Then we establish the a priori estimates and the existence of weak solutions by using a surjectivity result.

On the convergence of solutions of multivalued parabolic equations and applications

Abstract In this paper we examine parametric nonlinear parabolic problems with multivalued terms. Using a general notion of G-convergence for such operators we prove a convergence theorem for the solution sets of the corresponding Cauchy–Dirichlet problem. We also study a related minimax control problem.

Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions

In this paper the sensitivity of optimal solutions to control problems described by second order evolution subdifferential inclusions under perturbations of state relations and of cost functionals is investigated. First we establish a new existence result for a class of such inclusions. Then, based on the theory of sequential

Elements of Measure Theory

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