Download or read book Equivariant Degree with Symmetric Nonlinear Boundary Value Problems written by My Linh Nguyen and published by LAP Lambert Academic Publishing. This book was released on 2014-07-03 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary value/periodic problems for the nonlinear equation (or, more generally, second order nonlinear ODEs) have been the focus of nonlinear analysis study for a long time. The goal of this book is to show how the equivariant degree theory can be used for the systematic study of multiple solutions to several (symmetric) generalizations of BVP and for the classification of symmetric properties of these solutions. There are several classical methods of nonlinear analysis used to solve the BVP. However, their application encounters serious difficulties if: the group of symmetries is large, the dimension of the problem is high, and multiplicities of eigenvalues of linearizations are large, etc. In this book, we: (i) set up the abstract functional analysis framework for studying symmetric properties of multiple solutions to symmetric generalizations of the BV problem via the equivariant degree approach; (ii) describe wide classes of second order BVPs admitting dihedral symmetries to which the abstract theory can be effectively applied; (iii) and apply the obtained results to several classes of implicit second order symmetric differential equations.

Download or read book Symmetric Boundary Value Problems for Vector Nonlinear Pendulum Equation written by My Linh Nguyen and published by . This book was released on 2013 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results. In the dissertation, we: (i) set up the abstract functional analysis framework for studying symmetric properties of multiple solutions to symmetric generalizations of the problem (1) via the equivariant degree approach; (ii) describe wide classes of second order boundary value problems admitting dihedral symmetries to which the abstract theory can be effectively applied; and (iii) apply the obtained results to several classes of implicit second order symmetric differential equations. The abstract results are supported by concrete examples and numerical computations.

Download or read book Recent Trends in Nonlinear Analysis written by Alfonso Vignoli and published by Springer Science & Business Media. This book was released on 2000 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alfonso Vignoli - the Researcher, Teacher, and Friend.- How to Make Use of the Solution Set to Solve Boundary Value Problems.- On the Unique Solvability of Hammerstein Integral Equations with Non-Symmetric Kernels.- The Invariance of Domain for C1Fredholm Maps of Index Zero.- Positive Eigenfunctions for Some Unbounded Differential Operators.- Some Geometrical Properties of Rearrangement Invariant Spaces.- Strong Surjections and Nearness.- On the Vanishing Viscosity Approximation of a Time Dependent Hamilton-Jacobi Equation.- Some Remarks on a Nonlinear Model of Competitive Equilibrium.- Almost Discrete Convergence.- Nonlinear Stability of Eigenvalues of Compact Self-Adjoint Operators.- A Bifurcation Theorem for Lagrangian Intersections.- La valutazione di opzioni implicite nei mutui bancari.- Continuity of Near-Duality Maps and Characterizations of Ideal Spaces of Measurable Functions.- A Spectral Theory for Semilinear Operators and its Applications.- Feedback Stability of Closed Sets for Nonlinear Control Systems.- Two Mechanical Systems and Equivariant Degree.- On the Semilinear Dirichlet Problem for a Class of Nonlocal Operators Generating Dirichlet Forms.- Bifurcation for One-Parameter Families of Scalar Maps: A Geometric Viewpoint.- Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms.- Self-Similar Measures in Quasi-Metric Spaces.- C1-Fredholm Maps and Bifurcation for Quasilinear Elliptic Equations on$${\mathbb{R} n} $$.

Download or read book Topological Degree Methods in Nonlinear Boundary Value Problems written by J. Mawhin and published by American Mathematical Soc.. This book was released on 1979 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures from the CBMS Regional Conference held at Harvey Mudd College, June 1977. This monograph consists of applications to nonlinear differential equations of the author's coincidental degree. It includes an bibliography covering many aspects of the modern theory of nonlinear differential equations and the theory of nonlinear analysis.

Download or read book Equivariant Degree Theory written by Jorge Ize and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new degree theory for maps which commute with a group of symmetries. This degree is no longer a single integer but an element of the group of equivariant homotopy classes of maps between two spheres and depends on the orbit types of the spaces. The authors develop completely the theory and applications of this degree in a self-contained presentation starting with only elementary facts. The first chapter explains the basic tools of representation theory, homotopy theory and differential equations needed in the text. Then the degree is defined and its main abstract properties are derived. The next part is devoted to the study of equivariant homotopy groups of spheres and to the classification of equivariant maps in the case of abelian actions. These groups are explicitely computed and the effects of symmetry breaking, products and composition are thorougly studied. The last part deals with computations of the equivariant index of an isolated orbit and of an isolated loop of stationary points. Here differential equations in a variety of situations are considered: symmetry breaking, forcing, period doubling, twisted orbits, first integrals, gradients etc. Periodic solutions of Hamiltonian systems, in particular spring-pendulum systems, are studied as well as Hopf bifurcation for all these situations.

Download or read book Nonlinear Boundary Value Problems in Science and Engineering written by C. Rogers and published by Academic Press. This book was released on 1989-11-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overall, our object has been to provide an applications-oriented text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.

Download or read book Nonlinear Analysis and Optimization II written by Simeon Reich and published by American Mathematical Soc.. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the second of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in important fields of mathematics. This volume contains articles on optimization. Topics covered include the calculus of variations, constrained optimization problems, mathematical economics, metric regularity, nonsmooth analysis, optimal control, subdifferential calculus, time scales and transportation traffic. The companion volume (Contemporary Mathematics, Volume 513) is devoted to nonlinear analysis. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: J.-P. Aubin and S. Martin -- Travel time tubes regulating transportation traffic; R. Baier and E. Farkhi -- The directed subdifferential of DC functions; Z. Balanov, W. Krawcewicz, and H. Ruan -- Periodic solutions to $O(2)$-symmetric variational problems: $O(2) \times S^1$- equivariant gradient degree approach; J. F. Bonnans and N. P. Osmolovskii -- Quadratic growth conditions in optimal control problems; J. M. Borwein and S. Sciffer -- An explicit non-expansive function whose subdifferential is the entire dual ball; G. Buttazzo and G. Carlier -- Optimal spatial pricing strategies with transportation costs; R. A. C. Ferreira and D. F. M. Torres -- Isoperimetric problems of the calculus of variations on time scales; M. Foss and N. Randriampiry -- Some two-dimensional $\mathcal A$-quasiaffine functions; F. Giannessi, A. Moldovan, and L. Pellegrini -- Metric regular maps and regularity for constrained extremum problems; V. Y. Glizer -- Linear-quadratic optimal control problem for singularly perturbed systems with small delays; T. Maruyama -- Existence of periodic solutions for Kaldorian business fluctuations; D. Mozyrska and E. Paw'uszewicz -- Delta and nabla monomials and generalized polynomial series on time scales; D. Pallaschke and R. Urba'ski -- Morse indexes for piecewise linear functions; J.-P. Penot -- Error bounds, calmness and their applications in nonsmooth analysis; F. Rampazzo -- Commutativity of control vector fields and ""inf-commutativity""; A. J. Zaslavski -- Stability of exact penalty for classes of constrained minimization problems in finite-dimensional spaces. (CONM/514)

Download or read book Handbook of Differential Equations Ordinary Differential Equations written by Flaviano Battelli and published by Elsevier. This book was released on 2008-08-19 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. Covers a variety of problems in ordinary differential equations Pure mathematical and real-world applications Written for mathematicians and scientists of many related fields

Download or read book An Introduction to Nonlinear Boundary Value Problems written by Lakshmikantham and published by Academic Press. This book was released on 1974-05-31 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

Download or read book Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems written by Dumitru Motreanu and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.

Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.

Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.

Download or read book Theory of Degrees with Applications to Bifurcations and Differential Equations written by Wieslaw Krawcewicz and published by Wiley-Interscience. This book was released on 1997-02-05 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to degree theory and its applications to nonlinear differential equations. It uses an applications-oriented to address functional analysis, general topology and differential equations and offers a unified treatment of the classical Brouwer degree, the recently developed S?1-degree and the Dold-Ulrich degree for equivalent mappings and bifurcation problems. It integrates two seemingly disparate concepts, beginning with review material before shifting to classical theory and advanced application techniques.

Download or read book Nonlinear Two Point Boundary Value Problems written by Bailey and published by Academic Press. This book was released on 1968 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Two Point Boundary Value Problems

Download or read book Similarity Symmetry and Solutions of Nonlinear Boundary Value Problems written by and published by . This book was released on 1993 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topological Nonlinear Analysis written by Michele Matzeu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological tools in Nonlinear Analysis had a tremendous develop ment during the last few decades. The three main streams of research in this field, Topological Degree, Singularity Theory and Variational Meth ods, have lately become impetuous rivers of scientific investigation. The process is still going on and the achievements in this area are spectacular. A most promising and rapidly developing field of research is the study of the role that symmetries play in nonlinear problems. Symmetries appear in a quite natural way in many problems in physics and in differential or symplectic geometry, such as closed orbits for autonomous Hamiltonian systems, configurations of symmetric elastic plates under pressure, Hopf Bifurcation, Taylor vortices, convective motions of fluids, oscillations of chemical reactions, etc . . . Some of these problems have been tackled recently by different techniques using equivariant versions of Degree, Singularity and Variations. The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in Nonlinear Analysis during the last two-three decades. The survey articles presented here reflect the personal taste and points of view of the authors (all of them well-known and distinguished specialists in their own fields) on the subject matter. A common feature of these papers is that of start ing with an historical introductory background of the different disciplines under consideration and climbing up to the heights of the most recent re sults.