The Nonlinear Limit Point Limit Circle Problem
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The Nonlinear Limit Point Limit Circle Problem
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Author : Miroslav Bartusek
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
The Nonlinear Limit Point Limit Circle Problem written by Miroslav Bartusek 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 2011-06-27 with Mathematics categories.
This self-contained monograph traces the evolution of the limit–point/limit–circle problem from its 1910 inception, in a paper by Hermann Weyl, to its modern-day extensions to the asymptotic analysis of nonlinear differential equations. The authors distill the classical theorems in the linear case and carefully map the progress from linear to nonlinear limit–point results. The relationship between the limit–point/limit–circle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limit–point/limit–circle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields.
The Strong Nonlinear Limit Point Limit Circle Problem
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Author : Graef John R
language : en
Publisher: World Scientific
Release Date : 2017-10-06
The Strong Nonlinear Limit Point Limit Circle Problem written by Graef John R 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. Contents: The Origins of the Limit-Point/Limit-Circle ProblemEquations with p-LaplacianStrong Limit-Point/Limit-Circle PropertiesDamped EquationsHigher Order EquationsDelay Equations IDelay Equations IITransformations of the Basic EquationNotes, Open Problems, and Future Directions Readership: Graduate students and researchers of mathematics integrated in limit-point/limit circle topics. Keywords: Limit-Point Problem;Limit-Circle Problem;Strong Limit-Point Problem;Strong Limit-Circle Problem;Asymptotic Properties of Solutions;Nonlinear Differential Equations;Second Order Equations;Higher Order EquationsReview: Key Features: There is no other source of results on this problem except for the individual papers that appear in the literature. This work collects all that is known about this problem in one placeThe references on the nonlinear problem are complete up to 2017Directions for future research are indicated
Spectral Theory Of Differential Operators
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Author : I.W. Knowles
language : en
Publisher: Elsevier
Release Date : 1981-01-01
Spectral Theory Of Differential Operators written by I.W. Knowles and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Spectral Theory of Differential Operators
Pacific Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1983
Pacific Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Ordinary Differential Equations And Boundary Value Problems
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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 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 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. Contents: Systems of Differential EquationsContinuation of Solutions and Maximal Intervals of ExistenceSmooth Dependence on Initial Conditions and Smooth Dependence on a ParameterSome Comparison Theorems and Differential InequalitiesLinear Systems of Differential EquationsPeriodic Linear Systems and Floquet TheoryStability TheoryPerturbed Systems and More on Existence of Periodic Solutions Readership: Graduate students and researchers interested in ordinary differential equations. Keywords: Differential Equations;Linear Systems;Comparison Theorems;Differential Inequalities;Periodic Systems;Floquet Theory;Stability Theory;Perturbed Equations;Periodic SolutionsReview: Key Features: Clarity of presentationTreatment of linear and nonlinear problemsIntroduction to stability theoryNonroutine exercises to expand insight into more difficult conceptsExamples provided with thorough explanations
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems
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Author : Graef John R
language : en
Publisher: World Scientific
Release Date : 2018-09-18
Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems written by Graef John R 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.
An Index And Other Useful Information
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Author : A. Dold
language : en
Publisher: Springer
Release Date : 2013-12-11
An Index And Other Useful Information written by A. Dold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
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.
Communications On Applied Nonlinear Analysis
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Author :
language : en
Publisher:
Release Date : 2008
Communications On Applied Nonlinear Analysis written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Nonlinear functional analysis categories.
Panamerican Mathematical Journal
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Author :
language : en
Publisher:
Release Date : 2008
Panamerican Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.