This is the first monograph devoted to the variational analysis of nonlocal problems. The volume provides researchers and graduate students with a thorough introduction to variational and topological methods in the framework of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory. The key features of this new monograph are the following: (i) it presents a modern, unified approach to analyzing nonlocal equations; (ii) it examines a broad range of problems described by nonlocal operators that can be extended to other classes of related problems; and (iii) it reveals a number of surprising interactions among various topics. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 17642841

The aim of this monograph is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 18413657

The monograph develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolves in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 18463065

The monograph emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 18583897

The monographs covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods. Each of these topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. Problems are presented for each topic. The entire collection offers a balanced and useful picture for the application surrounding each topic. Encyclopedic coverage in mathematical analysis is the first of its kind and is accessible to a wide readership. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis. Remark: According to the Slovenian Research Agency (ARRS) criteria this book represents an outstanding research achievement, with the maximum possible score (A''=1).

COBISS.SI-ID: 17676121