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Variational, topological, and partial order methods with their applications

Author: Zhitao Zhang
Publisher: Berlin ; New York : Springer, ©2013.
Series: Developments in mathematics, v.29.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Zhang, Zhitao.
Variational, topological, and partial order methods with their applications.
Heidelberg ; New York : Springer, c2013
(DLC) 2012949194
(OCoLC)820964171
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Zhitao Zhang
ISBN: 9783642307096 3642307094 3642307086 9783642307089
OCLC Number: 811565964
Description: 1 online resource (xi, 330 p.)
Contents: Preliminaries --
Cone and Partial Order Methods --
Minimax Methods --
Bifurcation and Critical Point --
Solutions of a Class of Monge-Ampère Equations --
Topological Methods and Applications --
Dancer-Fučik Spectrum --
Sign-Changing Solutions --
Extension of Brezis-Nirenberg's Results and Quasilinear Problems --
Nonlocal Kirchhoff Elliptic Problems --
Free Boundary Problems, System of Equations for Bose-Einstein Condensate and Competing Species.
Series Title: Developments in mathematics, v.29.
Responsibility: Zhitao Zhang.

Abstract:

Covering leading-edge research, and with a focus on new developments in non-linear functional analysis, this is a vital addition to the literature that details theory as well as applications,  Read more...

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schema:description"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.Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, and mixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the author uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with a class of Monge-Ampère equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications is studied. Chapter 7 is devoted to the Dancer-Fucik spectrum. In Chapter 8, some results on sign-changing solutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, the focus is on free boundary problems, Schrödinger systems from Bose-Einstein condensate and competing systems with many species."
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