Topics In Nonlinear Analysis Applications

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.

New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.

This book develops methods which explore some new interconnections and interrelations between Analysis and Topology and their applications. Emphasis is given to several recent results which have been obtained mainly during the last years and which cannot be found in other books in Nonlinear Analysis. Interest in this subject area has rapidly increased over the last decade, yet the presentation of research has been confined mainly to journal articles.

This book develops methods which explore some new interconnections and interrelations between Analysis and Topology and their applications. Emphasis is given to several recent results which have been obtained mainly during the last years and which cannot be found in other books in Nonlinear Analysis. Interest in this subject area has rapidly increased over the last decade, yet the presentation of research has been confined mainly to journal articles. Contents:CONES AND COMPLEMENTARITY PROBLEMS:IntroductionConvex Cones:Normal ConesRegular and Completely Regular ConesWell Based ConesIsotone Projection ConesGalerkin ConesComplementarity Problems:The Explicit Complementarity ProblemThe Implicit Complementarity ProblemThe Generalized Order Complementarity ProblemExistence Theorems:Galerkin Cones and the Generalized Karamardian ConditionGalerkin Cones and Conically Coercive FunctionsVariational Inequalities and Explicit Complementarity ProblemsIsotone Projection Cones and Complementarity ProblemsCommentComplementarity Problems And Condition (S)1+S-Variational Inequalities and the Implicit Complementarity ProblemHeterotonic Operators and the Generalized Order Complementarity ProblemTopological Degree and ComplementaritySome Special Problems in Complementarity Theory:Boundedness of the Solution-SetSolution Which is the Least Element of the Feasible SetThe Cardinality of the Solution-SetNonexistence of SolutionSensitivity AnalysisNonlinear Complementarity and Quasi-EquilibriaComplementarity and Fixed PointsReferencesMETRICS ON CONVEX CONES:IntroductionHilbert's Projective MetricThompson's MetricWorking with Two ConesMonotone Semigroups and Metrics on ConesReferencesZERO-EPI MAPPINGS:IntroductionZero-Epi Mappings on Bounded SetsZero-Epi Mappings on the Whole SpaceZero-Epi Mappings on ConesZero-Epi Families of Mappings and OptimizationZero-Epi Mappings and Complementarity ProblemsZero-Epi Mappings and k-Set ContractionReferencesVARIATIONAL PRINCIPLES:IntroductionPreliminariesCritical Points for Dynamical SystemsVariants of Ekeland's Variational PrincipleThe Drop TheoremStrong Forms and Generalizations of Ekeland's PrincipleEquivalenciesEkeland's Variational Principle for Vector Valued FunctionApplications:Existence of Solutions for Minimizing ProblemsCoercivity ConditionA Global Variational Principle on ConesDensity ResultMountain Pass LemmaThe Bishop-Phelps TheoremClarke's Fixed Point TheoremBorwein's ε-PrincipleΦ-Accretive Operators and SurjectivityZabreiko-Krasnoselskii's TheoremThe Drop Property and the Geometry of Banach SpacesThe Drop Property for Arbitrary SetsReferencesMAXIMAL ELEMENT PRINCIPLES:IntroductionPreliminariesVariation on Zorn's Lemma:ApplicationsCommentsNew Maximal Element Principles:ApplicationsA Fixed Point Theorem for Ordered SetsMaximality And SolvabilityVariable Drops and General SolvabilityA Drop TheoremLipschitzianess TestsMaximal Element Principles and General Newton-Kantorovich ProcessesCommentsPareto EfficiencyReferences Readership: Mathematicians and physicists. keywords:Nonlinear Analysis;Cones;Complementarity;Zero-Epi Mappings;Variational and Maximal Principles “The book will undoubtedly be useful to all specialists and beginners in nonlinear analysis as a rich reference book and well as a source of new problems and ideas.” Mathematics Abstracts

This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.