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Author: K.C. Chang
Publisher: Springer Science & Business Media
ISBN: 1461203856
Category : Mathematics
Languages : en
Pages : 323
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Book Description
The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Author: K.C. Chang
Publisher: Springer Science & Business Media
ISBN: 1461203856
Category : Mathematics
Languages : en
Pages : 323
Get Book Here
Book Description
The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Author: K.C. Chang
Publisher: Birkhäuser
ISBN: 9781461203865
Category : Mathematics
Languages : en
Pages : 313
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Book Description
The book is based on my lecture notes "Infinite dimensional Morse theory and its applications", 1985, Montreal, and one semester of graduate lectures delivered at the University of Wisconsin, Madison, 1987. Since the aim of this monograph is to give a unified account of the topics in critical point theory, a considerable amount of new materials has been added. Some of them have never been published previously. The book is of interest both to researchers following the development of new results, and to people seeking an introduction into this theory. The main results are designed to be as self-contained as possible. And for the reader's convenience, some preliminary background information has been organized. The following people deserve special thanks for their direct roles in help ing to prepare this book. Prof. L. Nirenberg, who first introduced me to this field ten years ago, when I visited the Courant Institute of Math Sciences. Prof. A. Granas, who invited me to give a series of lectures at SMS, 1983, Montreal, and then the above notes, as the primary version of a part of the manuscript, which were published in the SMS collection. Prof. P. Rabinowitz, who provided much needed encouragement during the academic semester, and invited me to teach a semester graduate course after which the lecture notes became the second version of parts of this book. Professors A. Bahri and H. Brezis who suggested the publication of the book in the Birkhiiuser series.
Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 1493912461
Category : Mathematics
Languages : en
Pages : 555
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Book Description
As Richard Bellman has so elegantly stated at the Second International Conference on General Inequalities (Oberwolfach, 1978), “There are three reasons for the study of inequalities: practical, theoretical, and aesthetic.” On the aesthetic aspects, he said, “As has been pointed out, beauty is in the eye of the beholder. However, it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive.” The content of the Handbook focuses mainly on both old and recent developments on approximate homomorphisms, on a relation between the Hardy–Hilbert and the Gabriel inequality, generalized Hardy–Hilbert type inequalities on multiple weighted Orlicz spaces, half-discrete Hilbert-type inequalities, on affine mappings, on contractive operators, on multiplicative Ostrowski and trapezoid inequalities, Ostrowski type inequalities for the Riemann–Stieltjes integral, means and related functional inequalities, Weighted Gini means, controlled additive relations, Szasz–Mirakyan operators, extremal problems in polynomials and entire functions, applications of functional equations to Dirichlet problem for doubly connected domains, nonlinear elliptic problems depending on parameters, on strongly convex functions, as well as applications to some new algorithms for solving general equilibrium problems, inequalities for the Fisher’s information measures, financial networks, mathematical models of mechanical fields in media with inclusions and holes.
Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 1493911066
Category : Mathematics
Languages : en
Pages : 783
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Book Description
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Author: Eduard Zehnder
Publisher: European Mathematical Society
ISBN: 9783037190814
Category : Dynamics
Languages : en
Pages : 372
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Book Description
This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.
Author: Djairo G. de Figueiredo
Publisher: Springer Science & Business Media
ISBN: 3319028561
Category : Mathematics
Languages : en
Pages : 733
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Book Description
This volume presents a collection of selected papers by the prominent Brazilian mathematician Djairo G. de Figueiredo, who has made significant contributions in the area of Differential Equations and Analysis. His work has been highly influential as a challenge and inspiration to young mathematicians as well as in development of the general area of analysis in his home country of Brazil. In addition to a large body of research covering a variety of areas including geometry of Banach spaces, monotone operators, nonlinear elliptic problems and variational methods applied to differential equations, de Figueiredo is known for his many monographs and books. Among others, this book offers a sample of the work of Djairo, as he is commonly addressed, advancing the study of superlinear elliptic problems (both scalar and system cases), including questions on critical Sobolev exponents and maximum principles for non-cooperative elliptic systems in Hamiltonian form.
Author: Paul Biran
Publisher: Springer Science & Business Media
ISBN: 1402042663
Category : Mathematics
Languages : en
Pages : 476
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Book Description
The papers collected in this volume are contributions to the 43rd session of the Seminaire ́ de mathematiques ́ superieures ́ (SMS) on “Morse Theoretic Methods in Nonlinear Analysis and Symplectic Topology.” This session took place at the Universite ́ de Montreal ́ in July 2004 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together young researchers from various parts of the world and to present to them some of the most signi cant recent advances in these areas. More than 77 mathematicians from 17 countries followed the 12 series of lectures and participated in the lively exchange of ideas. The lectures covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian di?eomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere during the meeting. We also thank Ms. Diane Belanger ́ , our administrative assistant, for her help with the organi- tion and Mr. Andre ́ Montpetit, our technical editor, for his help in the preparation of the volume.
Author: Haim Brzis
Publisher: World Scientific
ISBN: 9812382623
Category : Mathematics
Languages : en
Pages : 300
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Book Description
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 1418, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University. 166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrvdinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Author: Haim Brezis
Publisher: World Scientific
ISBN: 9814486760
Category : Mathematics
Languages : en
Pages : 300
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Book Description
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period: August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was organized by Mathematical School of Peking University, Academy of Mathematics and System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai University, and Department of Mathematics of Shanxi University, and was sponsored by Shanxi Province Education Committee, Tian Yuan Mathematics Foundation, and Shanxi University.166 mathematicians from 21 countries and areas in the world attended the conference. 53 invited speakers and 30 contributors presented their lectures. This conference aims at an overview of the recent development in nonlinear analysis. It covers the following topics: variational methods, topological methods, fixed point theory, bifurcations, nonlinear spectral theory, nonlinear Schrödinger equations, semilinear elliptic equations, Hamiltonian systems, central configuration in N-body problems and variational problems arising in geometry and physics.
Author: Robert F. Brown
Publisher: Springer Science & Business Media
ISBN: 1402032226
Category : Mathematics
Languages : en
Pages : 966
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Book Description
This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
