Solvability Of Nonlinear Singular Problems For Ordinary Differential Equations
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Solvability Of Nonlinear Singular Problems For Ordinary Differential Equations
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Author : Irena Rachunkova
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2009
Solvability Of Nonlinear Singular Problems For Ordinary Differential Equations written by Irena Rachunkova and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Boundary value problems categories.
State Dependent Impulses
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Author : Irena Rachůnková
language : en
Publisher: Springer
Release Date : 2015-09-29
State Dependent Impulses written by Irena Rachůnková and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.
Nonlinear Singular Perturbation Phenomena
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Author : K. W. Chang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Singular Perturbation Phenomena written by K. W. Chang 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 2012-12-06 with Mathematics categories.
Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif ferential equations, by means of the consistent use of differential in equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.
Approximation Solvability Of Nonlinear Functional And Differential Equations
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Author : Wolodymyr V. Petryshyn
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Approximation Solvability Of Nonlinear Functional And Differential Equations written by Wolodymyr V. Petryshyn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions to the general theory of A-proper and pseudo-A-proper maps; develops the linear theory of A-proper maps; furnishes the best possible results for linear equations; establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results; provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings; shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space; presents the generalized topological degree theory for A-proper mappings; and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.;There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.
Singular Nonlinear Partial Differential Equations
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Author : Raymond Gérard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Nonlinear Partial Differential Equations written by Raymond Gérard 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 2012-12-06 with Mathematics categories.
The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations.
Half Linear Differential Equations
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Author : Ondrej Dosly
language : en
Publisher: Elsevier
Release Date : 2005-07-06
Half Linear Differential Equations written by Ondrej Dosly and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-06 with Mathematics categories.
The book presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE’s with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations. - The first complete treatment of the qualitative theory of half-linear differential equations. - Comparison of linear and half-linear theory. - Systematic approach to half-linear oscillation and asymptotic theory. - Comprehensive bibliography and index. - Useful as a reference book in the topic.
Singular Perturbation Methods For Ordinary Differential Equations
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Author : Robert E., Jr. O'Malley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Perturbation Methods For Ordinary Differential Equations written by Robert E., Jr. O'Malley 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 2012-12-06 with Mathematics categories.
This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations
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Author : Ding Tong-ren
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-08-13
Approaches To The Qualitative Theory Of Ordinary Differential Equations Dynamical Systems And Nonlinear Oscillations written by Ding Tong-ren and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
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.
Singular Partial Differential Equations
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Author : Abduhamid Dzhuraev
language : en
Publisher: CRC Press
Release Date : 1999-11-29
Singular Partial Differential Equations written by Abduhamid Dzhuraev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-29 with Science categories.
Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain. Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others. Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians.