Download or read book Theory of a Higher Order Sturm Liouville Equation written by Vladimir Kozlov and published by Springer. This book was released on 2006-11-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.
Download or read book Second Order Sturm Liouville Difference Equations and Orthogonal Polynomials written by Alouf Jirari and published by American Mathematical Soc.. This book was released on 1995 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir presents machinery for analyzing many discrete physical situations, and should be of interest to physicists, engineers, and mathematicians. We develop a theory for regular and singular Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. We discuss the self-adjointness of these problems as well as their abstract spectral resolution in the appropriate [italic capital]L2 setting, and give necessary and sufficient conditions for a second-order difference operator to be self-adjoint and have orthogonal polynomials as eigenfunctions.
Download or read book Sturm Liouville Theory written by Anton Zettl and published by American Mathematical Soc.. This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1836-1837 Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which started the subject now known as the Sturm-Liouville problem. In 1910 Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, the Sturm-Liouville theory remains an intensely active field of research, with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of knowledge about some aspects of this theory. To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed. An extensive list of references and examples is provided and numerous open problems are given. The list of examples includes those classical equations and functions associated with the names of Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, Morse, as well as examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.
Download or read book Sturm Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.
Download or read book Sturm Liouville Theory and its Applications written by Mohammed Al-Gwaiz and published by Springer Science & Business Media. This book was released on 2008-01-15 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2. The text’s presentation follows a clear, rigorous mathematical style that is highly readable. The author first establishes the basic results of Sturm-Liouville theory and then provides examples and applications to illustrate the theory. The final two chapters, on Fourier and Laplace transformations, demonstrate the use of the Fourier series method for representing functions to integral representations.
Download or read book Multiparameter Eigenvalue Problems written by F.V. Atkinson and published by CRC Press. This book was released on 2010-12-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problem
Download or read book Elementary Differential Equations with Boundary Value Problems written by William F. Trench and published by Thomson Brooks/Cole. This book was released on 2001 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Download or read book Inverse Sturm Liouville Problems written by Boris Moiseevič Levitan and published by VSP. This book was released on 1987 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in inverse problems of spectral analysis has increased considerably in recent years due to the applications to important non-linear equations in mathematical physics. This monograph is devoted to the detailed theory of inverse problems and methods of their solution for the Sturm-Liouville case. Chapters 1--6 contain proofs which are, in many cases, very different from those known earlier. Chapters 4--6 are devoted to inverse problems of quantum scattering theory with attention being focused on physical applications. Chapters 7--11 are based on the author's recent research on the theory of finite- and infinite-zone potentials. A chapter discussing the applications to the Korteweg--de Vries problem is also included. This monograph is important reading for all researchers in the field of mathematics and physics.
Download or read book An Extension of the Classical Sturm Liouville Theory written by Hans F. Weinberger and published by . This book was released on 1953 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiparameter Eigenvalue Problems written by F. V. Atkinson and published by CRC Press. This book was released on 2019-09-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory for more than 40 years. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, this book reflects much of Dr. Atkinson's final work. It covers the full multiparameter theory as applied to second-order linear equations and considers the spectral theory of multiparameter problems in detail for both regular and singular cases. Examples are illustrated using Maple(TM).
Download or read book Inverse Sturm Liouville Problems and Their Applications written by G. Freiling and published by Nova Biomedical Books. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.
Download or read book Special Functions and Generalized Sturm Liouville Problems written by Mohammad Masjed-Jamei and published by Springer Nature. This book was released on 2020-01-25 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses theoretical and applied aspects of Sturm-Liouville theory and its generalization. It introduces and classifies generalized Sturm-Liouville problems in three different spaces: continuous, discrete, and q-discrete spaces, focusing on special functions that are solutions of a regular or singular Sturm-Liouville problem. Further, it describes the conditions under which the usual Sturm-Liouville problems with symmetric solutions can be extended to a larger class, particularly highlighting the solutions of generalized problems that result in new orthogonal sequences of continuous or discrete functions. Sturm-Liouville theory is central to problems in many areas, such as engineering, mathematics, physics, and biology. This accessibly written book on the topic is a valuable resource for a broad interdisciplinary readership, from novices to experts.
Download or read book Method of Spectral Mappings in the Inverse Problem Theory written by V. A. Yurko and published by VSP. This book was released on 2002-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural science. This monograph deals with inverse problems of spectral analysis for ordinary differential equations and aims to present the main results on inverse spectral problems using the so-called method of spectral mappings, which is one of the main tools in inverse spectral theory.The book consists of three chapters and opens with the method of spectral mappings, presented in the simplest version for the Sturm-Liouville operator. The second chapter deals with the inverse problem of recovering higher-order differential operators of the form, on the half-line and on a finite interval. In this chapter the author introduces the so-called Weyl matrix, which is a generalization of the classical Weyl function for the selfadjoint second-order differential operator. The last chapter contains a study on inverse spectral problems for differential equations with nonlinear dependence on the spectral parameter.This monograph will be of value and interest to specialists in the field of inverse problems for differential equations.
Download or read book The Cauchy Problem for Higher Order Abstract Differential Equations written by Ti-Jun Xiao and published by Springer. This book was released on 2013-12-11 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
Download or read book Difference Equations Discrete Dynamical Systems and Applications written by Martin Bohner and published by Springer. This book was released on 2015-12-01 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.
Download or read book Emerging Applications of Differential Equations and Game Theory written by Alparslan Gök, S?rma Zeynep and published by IGI Global. This book was released on 2019-11-22 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Branches of mathematics and advanced mathematical algorithms can help solve daily problems throughout various fields of applied sciences. Domains like economics, mechanical engineering, and multi-person decision making benefit from the inclusion of mathematics to maximize utility and cooperation across disciplines. There is a need for studies seeking to understand the theories and practice of using differential mathematics to increase efficiency and order in the modern world. Emerging Applications of Differential Equations and Game Theory is a collection of innovative research that examines the recent advancements on interdisciplinary areas of applied mathematics. While highlighting topics such as artificial neuron networks, stochastic optimization, and dynamical systems, this publication is ideally designed for engineers, cryptologists, economists, computer scientists, business managers, mathematicians, mechanics, academicians, researchers, and students.
Download or read book Eigenfunction Expansions Associated with Second order Differential Equations written by Edward Charles Titchmarsh and published by . This book was released on 1962 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
