Variational Methods for Nonlocal Fractional Problems
Variational Methods for Nonlocal Fractional Problems

Author: Giovanni Molica Bisci

Publisher: Cambridge University Press

Published: 2016-03-11

Total Pages: 401

ISBN-13: 1316571696

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This book provides researchers and graduate students with a thorough introduction to the variational analysis 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.

Nonlinear Analysis and Global Optimization
Nonlinear Analysis and Global Optimization

Author: Themistocles M. Rassias

Publisher: Springer Nature

Published: 2021-02-26

Total Pages: 484

ISBN-13: 3030617327

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This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

Equilibrium Problems and Applications
Equilibrium Problems and Applications

Author: Gábor Kassay

Publisher: Academic Press

Published: 2018-10-09

Total Pages: 442

ISBN-13: 0128110309

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Equilibrium Problems and Applications 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 evolved 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. - A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics - Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs - Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets - Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn

Basic Monotonicity Methods with Some Applications
Basic Monotonicity Methods with Some Applications

Author: Marek Galewski

Publisher: Springer Nature

Published: 2021-09-01

Total Pages: 183

ISBN-13: 3030753085

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This textbook introduces some basic tools from the theory of monotone operators together with some of their applications. Examples that work for ordinary differential equations are provided. The illustrating material is kept relatively simple, while at the same time offering inspiring applications to the reader. The material will appeal to graduate students in mathematics who want to learn some basics in the theory of monotone operators. Furthermore, it offers a smooth transition to studying more advanced topics pertaining to more refined applications by shifting to pseudomonotone operators, and next, to multivalued monotone operators.

Nonlinear Fractional Schrödinger Equations in R^N
Nonlinear Fractional Schrödinger Equations in R^N

Author: Vincenzo Ambrosio

Publisher: Springer Nature

Published: 2021-04-19

Total Pages: 669

ISBN-13: 3030602206

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This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.

Integro-Differential Elliptic Equations
Integro-Differential Elliptic Equations

Author: Xavier Fernández-Real

Publisher: Springer Nature

Published: 2024

Total Pages: 409

ISBN-13: 3031542428

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Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters

Fractional Calculus: Theory and Applications
Fractional Calculus: Theory and Applications

Author: Francesco Mainardi

Publisher: MDPI

Published: 2018-09-20

Total Pages: 209

ISBN-13: 3038972061

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This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics

Nonlinear Problems with Lack of Compactness
Nonlinear Problems with Lack of Compactness

Author: Giovanni Molica Bisci

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-02-08

Total Pages: 191

ISBN-13: 3110648938

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This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications
Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications

Author: El Hassan Zerrik

Publisher: Springer Nature

Published: 2019-08-26

Total Pages: 274

ISBN-13: 3030261492

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This book describes recent developments in a wide range of areas, including the modeling, analysis and control of dynamical systems, and explores related applications. The book provided a forum where researchers have shared their ideas, results on theory, and experiments in application problems. The current literature devoted to dynamical systems is quite large, and the authors’ choice for the considered topics was motivated by the following considerations. Firstly, the mathematical jargon for systems theory remains quite complex and the authors feel strongly that they have to maintain connections between the people of this research field. Secondly, dynamical systems cover a wider range of applications, including engineering, life sciences and environment. The authors consider that the book is an important contribution to the state of the art in the fuzzy and dynamical systems areas.