Partial Ordering Methods In Nonlinear Problems
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Partial Ordering Methods In Nonlinear Problems
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Author : Dajun Guo
language : en
Publisher: Nova Publishers
Release Date : 2004
Partial Ordering Methods In Nonlinear Problems written by Dajun Guo and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Special Interest Categories: Pure and applied mathematics, physics, optimisation and control, mechanics and engineering, nonlinear programming, economics, finance, transportation and elasticity. The usual method used in studying nonlinear problems such as topological method, variational method and others are generally only suited to the nonlinear problems with continuity and compactness. However, a lots of the problems appeared in theory and applications have no continuity and compactness, For example, differential equations and integral equations in infinite dimensional spaces, various equations defined on unbounded region are generally having no compactness. The problems can been divided into three types as follows: (1) Without using compact conditions but only using some inequalities related to some ordering, the existence and uniqueness of the fixed point for increasing operators, decreasing operators and mixed monotone operators, and the convergence of the iterative sequence are obtained. Also, these results have been used to nonlinear integral equations defined on unbounded regions. (2) Without using continuity conditions but only using a very relaxed weakly compact conditions, some new fixed point theorem of increasing operators are obtained. We have applied these results to nonlinear equations with discontinuous terms. (3) They systemly use the partial ordering methods to nonlinear integro-differential equations (include impulsive type) in Banach space.
Variational Topological And Partial Order Methods With Their Applications
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Author : Zhitao Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17
Variational Topological And Partial Order Methods With Their Applications written by Zhitao Zhang 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 2012-09-17 with Mathematics categories.
Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Order Structure And Topological Methods In Nonlinear Partial Differential Equations
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Author : Yihong Du
language : en
Publisher: World Scientific
Release Date : 2006
Order Structure And Topological Methods In Nonlinear Partial Differential Equations written by Yihong Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
Variational Methods In Partially Ordered Spaces
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Author : Alfred Göpfert
language : en
Publisher: Springer Nature
Release Date : 2023-12-08
Variational Methods In Partially Ordered Spaces written by Alfred Göpfert and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-08 with Business & Economics categories.
This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.
Order Structure And Topological Methods In Nonlinear Partial Differential Equations
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Author : Yihong Du
language : en
Publisher:
Release Date : 2006
Order Structure And Topological Methods In Nonlinear Partial Differential Equations written by Yihong Du and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations, Nonlinear categories.
Nonlinear Partial Differential Equations Of Second Order
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Author : Guangchang Dong
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Nonlinear Partial Differential Equations Of Second Order written by Guangchang Dong 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 1991 with Mathematics categories.
Addresses a class of equations central to many areas of mathematics and its applications. This book addresses a general approach that consists of the following: choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution.
Monotone Iterative Techniques For Discontinuous Nonlinear Differential Equations
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Author : V. Lakshmikantham
language : en
Publisher: Routledge
Release Date : 2017-09-29
Monotone Iterative Techniques For Discontinuous Nonlinear Differential Equations written by V. Lakshmikantham and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-29 with Mathematics categories.
""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.
Fixed Point Theory In Ordered Sets And Applications
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Author : Siegfried Carl
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
Fixed Point Theory In Ordered Sets And Applications written by Siegfried Carl 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 2010-11-17 with Mathematics categories.
This monograph provides a unified and comprehensive treatment of an order-theoretic fixed point theory in partially ordered sets and its various useful interactions with topological structures. The material progresses systematically, by presenting the preliminaries before moving to more advanced topics. In the treatment of the applications a wide range of mathematical theories and methods from nonlinear analysis and integration theory are applied; an outline of which has been given an appendix chapter to make the book self-contained. Graduate students and researchers in nonlinear analysis, pure and applied mathematics, game theory and mathematical economics will find this book useful.
Variational Topological And Partial Order Methods With Their Applications
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Author : Zhitao Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-18
Variational Topological And Partial Order Methods With Their Applications written by Zhitao Zhang 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 2012-09-18 with Mathematics categories.
Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Transformation Methods For Nonlinear Partial Differential Equations
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Author : Dominic G B Edelen
language : en
Publisher: World Scientific
Release Date : 1992-06-09
Transformation Methods For Nonlinear Partial Differential Equations written by Dominic G B Edelen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-09 with Science categories.
The purpose of the book is to provide research workers in applied mathematics, physics, and engineering with practical geometric methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of contact manifolds rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent publications of the authors'. The text contains numerous fully worked examples so that the reader can fully appreciate the power and scope of the new methods. In effect, the problem of solving systems of nonlinear partial differential equations is reduced to the problem of solving families of autonomous ordinary differential equations. This allows the graphs of solutions of the system of partial differential equations to be realized as certain leaves of a foliation of an appropriately defined contact manifold. In fact, it is often possible to obtain families of solutions whose graphs foliate an open subset of the contact manifold. These ideas are extended in the final chapter by developing the theory of transformations that map a foliation of a contact manifold onto a foliation. This analysis gives rise to results of surprising depth and practical significance. In particular, an extended Hamilton-Jacobi method for solving systems of partial differential equations is obtained.