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Author: Paul W. Eloe
Publisher: World Scientific
ISBN: 9814733482
Category : Mathematics
Languages : en
Pages : 249
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Book Description
"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--
Author: Paul W. Eloe
Publisher: World Scientific
ISBN: 9814733482
Category : Mathematics
Languages : en
Pages : 249
Get Book Here
Book Description
"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 408
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Book Description
Author: John R. Graef
Publisher: CRC Press
ISBN: 0429822618
Category : Mathematics
Languages : en
Pages : 425
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Book Description
Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.
Author: T. A. Lamke
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 416
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Book Description
Author: W. H. Shafer
Publisher: Plenum Publishing Corporation
ISBN: 9780306443480
Category : Education
Languages : en
Pages : 392
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Book Description
Masters Theses Listed by Discipline: Aerospace Engineering. Agricultural Economics, Sciences and Engineering. Architechtural Engineering and Urban Planning. Astronomy. Astrophysics. Ceramic Engineering. Communications Engineering and Computer Science. Cryogenic Engineering. Electrical Engineering. Engineering Mechanics. Engineering Physics. Engineering Science. Fuels, Combustion, and Air Pollution. General and Environmental Engineering. Geochemistry and Soil Science. Geological Sciences and Geophysical Engineering. Geology and Earth Science. Geophysics. Industrial Engineering. Marine and Ocean Engineering. Materials Science and Engineering. Mechanical Engineering and Bioengineering. Metallurgy. Meteorology and Atmospheric Science. 17 additional disciplines. Index.
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 432
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 784
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Book Description
Author: Gerald Teschl
Publisher: American Mathematical Society
ISBN: 147047641X
Category : Mathematics
Languages : en
Pages : 370
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Book Description
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Author: John R Graef
Publisher: World Scientific
ISBN: 9813274042
Category : Mathematics
Languages : en
Pages : 343
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Book Description
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.
Author: Ilja N. Bronštejn
Publisher: Springer
ISBN: 3662256517
Category : Technology & Engineering
Languages : en
Pages : 989
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Book Description
