This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many appli

This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.

This book is the first to discuss complementarity theory and variational inequalities using Leray–Schauder type alternatives. Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics. The ideas and method presented in this book may be considered as a starting point for new developments. The book presents a new kind of application for the Leray–Schauder principle.

An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.

Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.

This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.

This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of axiomatic measures of weak noncompactness. The authors continue to present some fixed point theorems in a nonempty closed convex of any Banach algebras or Banach algebras satisfying a sequential condition (P) for the sum and the product of nonlinear weakly sequentially continuous operators, and illustrate the theory by considering functional integral and partial differential equations. The existence of fixed points, nonlinear Leray–Schauder alternatives for different classes of nonlinear (ws)-compact operators (weakly condensing, 1-set weakly contractive, strictly quasi-bounded) defined on an unbounded closed convex subset of a Banach space are also discussed. The authors also examine the existence of nonlinear eigenvalues and eigenvectors, as well as the surjectivity of quasibounded operators. Finally, some approximate fixed point theorems for multivalued mappings defined on Banach spaces. Weak and strong topologies play a role here and both bounded and unbounded regions are considered. The authors explicate a method developed to indicate how to use approximate fixed point theorems to prove the existence of approximate Nash equilibria for non-cooperative games. Fixed point theory is a powerful and fruitful tool in modern mathematics and may be considered as a core subject in nonlinear analysis. In the last 50 years, fixed point theory has been a flourishing area of research. As such, the monograph begins with an overview of these developments before gravitating towards topics selected to reflect the particular interests of the authors.

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

This monograph explores the concept of the Brouwer degree and its continuing impact on the development of important areas of nonlinear analysis. The authors define the degree using an analytical approach proposed by Heinz in 1959 and further developed by Mawhin in 2004, linking it to the Kronecker index and employing the language of differential forms. The chapters are organized so that they can be approached in various ways depending on the interests of the reader. Unifying this structure is the central role the Brouwer degree plays in nonlinear analysis, which is illustrated with existence, surjectivity, and fixed point theorems for nonlinear mappings. Special attention is paid to the computation of the degree, as well as to the wide array of applications, such as linking, differential and partial differential equations, difference equations, variational and hemivariational inequalities, game theory, and mechanics. Each chapter features bibliographic and historical notes, and the final chapter examines the full history. Brouwer Degree will serve as an authoritative reference on the topic and will be of interest to professional mathematicians, researchers, and graduate students.