Nonlinear Differential Equations In Ordered Spaces

Author : S. Carl,Seppo Heikkila
Publisher : CRC Press
Page : 338 pages
File Size : 55,8 Mb
Release : 2000-06-14
Category : Mathematics
ISBN : 1584880686

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Nonlinear Differential Equations in Ordered Spaces by S. Carl,Seppo Heikkila Pdf

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data. The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods. Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.

Author : S. Carl,Seppo Heikkila
Publisher : CRC Press
Page : 336 pages
File Size : 47,6 Mb
Release : 2000-06-14
Category : Mathematics
ISBN : 9781482280951

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Nonlinear Differential Equations in Ordered Spaces by S. Carl,Seppo Heikkila Pdf

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data. The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods. Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.

Author : Yihong Du
Publisher : World Scientific
Page : 202 pages
File Size : 46,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812774446

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Order Structure and Topological Methods in Nonlinear Partial Differential Equations by Yihong Du Pdf

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. Sample Chapter(s). Chapter 1: Krein-Rutman Theorem and the Principal Eigenvalue (128 KB). Contents: KreinOCoRutman Theorem and the Principal Eigenvalue; Maximum Principles Revisited; The Moving Plane Method; The Method of Upper and Lower Solutions; The Logistic Equation; Boundary Blow-Up Problems; Symmetry and Liouville Type Results Over Half and Entire Spaces. Readership: Researchers and postgraduate students in partial differential equations."

Author : Svatopluk Fucik,Alois Kufner
Publisher : Elsevier
Page : 360 pages
File Size : 41,6 Mb
Release : 2014-12-03
Category : Technology & Engineering
ISBN : 9781483278377

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Nonlinear Differential Equations by Svatopluk Fucik,Alois Kufner Pdf

Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

Author : Thomas Runst,Winfried Sickel
Publisher : Walter de Gruyter
Page : 561 pages
File Size : 46,7 Mb
Release : 2011-07-22
Category : Mathematics
ISBN : 9783110812411

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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by Thomas Runst,Winfried Sickel Pdf

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

Author : Julii A. Dubinskii
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 42,7 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 9027721475

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Sobolev Spaces of Infinite Order and Differential Equations by Julii A. Dubinskii Pdf

Author : Thomas Runst,Winfried Sickel
Publisher : Walter de Gruyter
Page : 568 pages
File Size : 55,9 Mb
Release : 1996
Category : Mathematics
ISBN : 3110151138

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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations by Thomas Runst,Winfried Sickel Pdf

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dłotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Author : J. Kurzweil
Publisher : Elsevier
Page : 440 pages
File Size : 45,7 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483297651

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Ordinary Differential Equations by J. Kurzweil Pdf

The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations. The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 41,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : Guangchang Dong
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 51,8 Mb
Release : 1991
Category : Mathematics
ISBN : 0821845543

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Nonlinear Partial Differential Equations of Second Order by Guangchang Dong Pdf

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.

Author : V. Lakshmikantham,S. Leela
Publisher : Pergamon
Page : 276 pages
File Size : 50,9 Mb
Release : 1981
Category : Banach spaces
ISBN : UCAL:B4406400

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Nonlinear Differential Equations in Abstract Spaces by V. Lakshmikantham,S. Leela Pdf

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations

Author : Pavel Drabek,Pavel Krejci,Peter Takac
Publisher : CRC Press
Page : 212 pages
File Size : 51,8 Mb
Release : 1999-05-20
Category : Mathematics
ISBN : 1584880368

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Nonlinear Differential Equations by Pavel Drabek,Pavel Krejci,Peter Takac Pdf

Working with mathematical models today requires in-depth knowledge of recent methods developed for solving nonlinear differential equations. Keeping abreast of these developments is the goal of the regular meetings of nonlinear analysts held in the Czech Republic, the most recent of which formed the basis of this volume. The subject addressed by these authors is the theory of nonlinear differential equations, with focus on the quasilinear elliptic differential equations of the degenerate type. Their topics include:

Author : Tran Duc Van,Dinh Nho Hào
Publisher : World Scientific
Page : 248 pages
File Size : 42,8 Mb
Release : 1994-04-29
Category : Mathematics
ISBN : 9789814502504

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Differential Operators of Infinite Order with Real Arguments and Their Applications by Tran Duc Van,Dinh Nho Hào Pdf

This book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis. Part I develops the theory of pseudodifferential operators with real analytic symbols, the local representatives of which are linear differential operators of infinite order acting in the spaces of basic and generalized functions based on the duality of the spaces of real analytic functions and functionals. Applications to a variety of problems of PDEs and numerical analysis are given. Part II is devoted to the theory of Sobolev-Orlicz spaces of infinite order and the solvability of nonlinear partial differential equations with arbitrary nonlinearities. Contents:PreliminariesPseudo-Differential Operators with Real Analytic SymbolsApplications to Pseudo-Differential EquationsApproximation MethodsA Mollification Method for Ill-Posed ProblemsNontriviality of Sobolev-Orlicz Spaces of Infinite OrderSome Properties of Sobolev-Orlicz Spaces of Infinite OrderElliptic Equations of Infinite Order with Arbitrary Nonlinearities Readership: Mathematicians, engineers and physicists. keywords:Pseudo-Differential Operators with Real Analytic Symbols;Pseudo-Differential Equations;Approximation Methods;Mollification Method for Ill-Posed Problems;Sobolev-Orlicz Spaces of Infinite Order;Elliptic Equations of Infinite Order with Arbitrary Nonlinearities

Author : V. Lakshmikantham
Publisher : Routledge
Page : 265 pages
File Size : 54,8 Mb
Release : 2017-09-29
Category : Mathematics
ISBN : 9781351430159

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Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations by V. Lakshmikantham Pdf

""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.

Author : Dajun Guo,Yeol Je Cho,Jiang Zhu
Publisher : Nova Publishers
Page : 362 pages
File Size : 52,5 Mb
Release : 2004
Category : Mathematics
ISBN : 1594540187

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Partial Ordering Methods in Nonlinear Problems by Dajun Guo,Yeol Je Cho,Jiang Zhu Pdf

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.