An Introduction To Minimax Theorems And Their Applications To Differential Equations
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An Introduction To Minimax Theorems And Their Applications To Differential Equations
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Author : Maria do Rosário Grossinho
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
An Introduction To Minimax Theorems And Their Applications To Differential Equations written by Maria do Rosário Grossinho and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.
An Introduction To Minimax Theorems And Their Applications To Differential Equations
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Author : Maria do Rosário Grossinho
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-28
An Introduction To Minimax Theorems And Their Applications To Differential Equations written by Maria do Rosário Grossinho and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-28 with Mathematics categories.
The book is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: To present a survey of existing minimax theorems, To give applications to elliptic differential equations in bounded domains, To consider the dual variational method for problems with continuous and discontinuous nonlinearities, To present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities, To study homoclinic solutions of differential equations via the variational methods. The contents of the book consist of seven chapters, each one divided into several sections. Audience: Graduate and post-graduate students as well as specialists in the fields of differential equations, variational methods and optimization.
Minimax Theorems
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Author : Michel Willem
language : en
Publisher: Birkhäuser
Release Date : 1997-02-01
Minimax Theorems written by Michel Willem and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-01 with Mathematics categories.
A textbook for an advanced graduate course in partial differential equations. Presents basic minimax theorems starting from a quantitative deformation lemma; and demonstrates their applications to partial differential equations, particularly in problems dealing with a lack of compactness. Includes some previously unpublished results such as a treatment of the generalized Kadomtsev-Petviashvili equation. Annotation copyright by Book News, Inc., Portland, OR
Minimax Methods In Critical Point Theory With Applications To Differential Equations
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Author : Paul H. Rabinowitz
language : en
Publisher: American Mathematical Soc.
Release Date : 1986-07-01
Minimax Methods In Critical Point Theory With Applications To Differential Equations written by Paul H. Rabinowitz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-07-01 with Mathematics categories.
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
An Introduction To Nonlinear Analysis
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Author : Martin Schechter
language : en
Publisher: Cambridge University Press
Release Date : 2004
An Introduction To Nonlinear Analysis written by Martin Schechter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The techniques that can be used to solve non-linear problems are far different than those that are used to solve linear problems. Many courses in analysis and applied mathematics attack linear cases simply because they are easier to solve and do not require a large theoretical background in order to approach them. Professor Schechter's 2005 book is devoted to non-linear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving non-linear problems is developed whilst demonstrating their application to problems in one dimension and then leading to higher dimensions. The reader is guided using simple exposition and proof, assuming a minimal set of pre-requisites. For completion, a set of appendices covering essential basics in functional analysis and metric spaces is included, making this ideal as an accompanying text on an upper-undergraduate or graduate course, or even for self-study.
Minimax Theorems
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Author : Michel Willem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Minimax Theorems written by Michel Willem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Many boundary value problems are equivalent to Au=O (1) where A : X --+ Y is a mapping between two Banach spaces. When the problem is variational, there exists a differentiable functional rand inf.
Hyperfinite Dirichlet Forms And Stochastic Processes
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
Hyperfinite Dirichlet Forms And Stochastic Processes written by Sergio Albeverio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Mathematics categories.
This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.
Stochastic Approximation And Its Applications
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Author : Han-Fu Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-30
Stochastic Approximation And Its Applications written by Han-Fu Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-30 with Mathematics categories.
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Minimax And Applications
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Author : Ding-Zhu Du
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-10-31
Minimax And Applications written by Ding-Zhu Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-31 with Computers categories.
Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1) ",EX !lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x,y) = maxminf(x,y). (2) "'EX !lEY !lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in linear and convex quadratic programming interprets minimax theory in a different way. The second issue concerns the establishment of sufficient and necessary conditions for values of the variables x and y that achieve the global minimax function value f(x*, y*) = minmaxf(x, y). (3) "'EX !lEY There are two developments in minimax theory that we would like to mention.
Minimax Theorems And Qualitative Properties Of The Solutions Of Hemivariational Inequalities
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Author : Dumitru Motreanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Minimax Theorems And Qualitative Properties Of The Solutions Of Hemivariational Inequalities written by Dumitru Motreanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Boundary value problems which have variational expressions in form of inequal ities can be divided into two main classes. The class of boundary value prob lems (BVPs) leading to variational inequalities and the class of BVPs leading to hemivariational inequalities. The first class is related to convex energy functions and has being studied over the last forty years and the second class is related to nonconvex energy functions and has a shorter research "life" beginning with the works of the second author of the present book in the year 1981. Nevertheless a variety of important results have been produced within the framework of the theory of hemivariational inequalities and their numerical treatment, both in Mathematics and in Applied Sciences, especially in Engineering. It is worth noting that inequality problems, i. e. BVPs leading to variational or to hemivariational inequalities, have within a very short time had a remarkable and precipitate development in both Pure and Applied Mathematics, as well as in Mechanics and the Engineering Sciences, largely because of the possibility of applying and further developing new and efficient mathematical methods in this field, taken generally from convex and/or nonconvex Nonsmooth Analy sis. The evolution of these areas of Mathematics has facilitated the solution of many open questions in Applied Sciences generally, and also allowed the formu lation and the definitive mathematical and numerical study of new classes of interesting problems.