Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions Functional Problems And Applications
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Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions Functional Problems And Applications
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Author : Feliz Manuel Minhos
language : en
Publisher: World Scientific
Release Date : 2017-08-23
Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions Functional Problems And Applications written by Feliz Manuel Minhos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators.The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line.Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases.The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved.
Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions
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Author : Feliz Manuel Minhós
language : en
Publisher:
Release Date : 2017
Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions written by Feliz Manuel Minhós and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Boundary value problems categories.
"This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm–Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators. The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line. Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases. The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved."--Publisher's website.
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems
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Author : John R Graef
language : en
Publisher: World Scientific
Release Date : 2018-09-18
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems written by John R Graef and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Mathematics categories.
The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.
Ordinary Differential Equations And Boundary Value Problems Volume I Advanced Ordinary Differential Equations
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Author : John R Graef
language : en
Publisher: World Scientific
Release Date : 2018-02-13
Ordinary Differential Equations And Boundary Value Problems Volume I Advanced Ordinary Differential Equations written by John R Graef and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.
The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book.The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well.Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems.Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2008-10-06
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-06 with Mathematics categories.
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Boundary Value Problems For Fractional Differential Equations And Systems
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Author : Bashir Ahmad
language : en
Publisher: World Scientific
Release Date : 2021-02-18
Boundary Value Problems For Fractional Differential Equations And Systems written by Bashir Ahmad and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-18 with Mathematics categories.
This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
The Strong Nonlinear Limit Point Limit Circle Problem
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Author : John R Graef
language : en
Publisher: World Scientific
Release Date : 2017-10-06
The Strong Nonlinear Limit Point Limit Circle Problem written by John R Graef and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-06 with Mathematics categories.
The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated.
Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains
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Author : Feliz Manuel Minhos
language : en
Publisher: World Scientific
Release Date : 2022-04-11
Nonlinear Higher Order Differential And Integral Coupled Systems Impulsive And Integral Equations On Bounded And Unbounded Domains written by Feliz Manuel Minhos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Mathematics categories.
Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.
Solving Problems In Multiply Connected Domains
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Author : Darren Crowdy
language : en
Publisher: SIAM
Release Date : 2020-04-20
Solving Problems In Multiply Connected Domains written by Darren Crowdy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-20 with Mathematics categories.
Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
Boundary Value Problems With Equivalued Surface And Resistivity Well Logging
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Author : T Li
language : en
Publisher: CRC Press
Release Date : 1998-03-25
Boundary Value Problems With Equivalued Surface And Resistivity Well Logging written by T Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-25 with Mathematics categories.
This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.