5 edition of **Theory of Branching of Solutions of Nonlinear Equations (Monographs and textbooks on pure and applied mathematics)** found in the catalog.

- 321 Want to read
- 35 Currently reading

Published
**December 1974**
by Wolters-Noordhoff B.V.
.

Written in English

- Calculus,
- Mathematics

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 510 |

ID Numbers | |

Open Library | OL9075071M |

ISBN 10 | 9001882803 |

ISBN 10 | 9789001882808 |

A further restriction is that the series coefficients will be specified by a nonlinear recurrence (the nonlinearities are inherited from the differential equation). In order for the solution method to work, as in linear equations, it is necessary to express every term in the nonlinear equation as a power series so that all of the terms may be. Significantly, Schulze's theory admits a parameter-dependent version, which allows the description of the branching behaviour in time of discrete asymptotics of solutions near conical points. The calculus is presented in a form in which the operators are permitted to have symbols with limited smoothness, as arises in nonlinear problems.

It is proved that there are many quasi-periodic solutions with Liouvillean frequency for the above equation. The proof is based on an infinite dimensional KAM Theorem. The study on periodic solutions for ordinary differential equations is a very important branch in the differential equation theory. Many results about the existence of periodic solutions for second-order differential equations have been obtained by combining the classical method of lower and upper solutions and the method of alternative problems (The Lyapunov-Schmidt method) as .

B. M. Podlevskyi (October 24th ). Numerical Algorithms of Finding the Branching Lines and Bifurcation Points of Solutions for One Class of Nonlinear Integral Equations, Nonlinearity, Bifurcation and Chaos - Theory and Applications, Jan Awrejcewicz and Peter Hagedorn, IntechOpen, DOI: / Available from. Introduction to Non-Linear Algebra n and v ITEP, Moscow, Russia ABSTRACT Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps. This powerful science is .

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Additional Physical Format: Online version: Vaĭnberg, M.M. (Mordukhaĭ Moiseevich). Theory of branching of solutions of non-linear equations. Leyden, Noordhoff International Pub.

Theory of branching of solutions of non-linear equations (Monographs and textbooks on pure and applied mathematics) Hardcover – January 1, by M.

M Vaĭnberg (Author) See all formats and editions Hide other formats and editions. Price New from Used from Cited by: Vainberg, M.

& Trenogin, V.Theory of branching of solutions of non-linear equations. [By] M. Vainberg and V. Trenogin. Translated by Israel Program for Scientific Translations Noordhoff International Pub Leyden. Wikipedia Citation. Theory of Probability & Its Applications. Browse TVP; FAQ; E-books.

Browse e-books; Wave Equation Stabilization by Delays Equal to Even Multiples of the Wave Propagation Time Theory of Branching of Solutions of Non-Linear Equations (M.

Cited by: This diverse class of degenerate PDEs embraces equations of different three types: parabolic, hyperbolic, and nonlinear dispersion. Such degenerate evolution equations from various applications in mechanics and physics admitting compactly supported and blow-up solutions attracted attention of the mathematicians since the s.

Branching, i.e., the splitting of solutions into two or more branches, is considered to be the essential feature of nonlinear boundary problems solutions behaviour for deformation of thin shells.

The types of branching and branching (singular) points are distinguished as bifurcation points and limit points. A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related.

The authors introduce the reader to the theory and then. This includes the precise properties of the set of solutions such as: the exact description of the bifurcation of equilibrium points and limit cycles for ordinary differential equations, the multiplicity of solutions to nonlinear elliptic equations, the number of periodic solutions appearing from perturbations of Hamiltonian systems, and the.

() Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations. Journal of Nonlinear Science The branching theory of solutions to nonlinear equations is considered for symmetry breaking problems with the passage of a bifurcation parameter through a critical values, forming solutions with.

solution in a closed form. Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods. More than integral equations and their solutions are given in the ﬁrst part of the book (Chapters 1–6).

A lot of new exact solutions to linear and nonlinear equations are included. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations.

Unlike comparable books that typically only use formal. Numerical analysis of the branching of solutions to nonlinear equations for cylindrical shells Article (PDF Available) in International Applied Mechanics 42(1) January with 25 Reads.

This book is designed to introduce some important methods for non-linear evolution equations. The material in this book has been used in as well as in other branches of science. This book aims to concisely explain in a clear and easily and outline the theory of global solutions, which is the main concern of this book.

In this chapter we. Many physical problems lead to boundary value problems for nonlinear differential equations, which depend upon a parameter and which for certain values of the parameter admit multiple solutions.

For example, the problem may admit a trivial state as a solution and at certain values of the parameter nontrivial solution branches will bifurcate.

simple, reasonably general, nonlinear system theory could be developed. Hand in hand with this viewpoint was the feeling that many of the approaches useful for linear systems ought to be extensible to the nonlinear theory.

This is a key point if the theory is to. The presen t volume contains the book-length text of a paper entitled "Nonlinear operators and nonlinear equations of evolution in Banach spaces" composed in its entiret y during the calendar year to be publishe d as par t of the Proceedings of the Symposium on Nonlinear Functional Analysis held in connection with the.

[1] Moncef Aouadi, Alain -stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations & Control Theory,4 (3): doi: /eect [2]. smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold.

First, the iterative numerical method based on the modiﬁed Newton–Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations.

Nonlinear Differential Equations and Nonlinear Mechanics provides information pertinent to nonlinear differential equations, nonlinear mechanics, control theory, and other related topics. This book discusses the properties of solutions of equations in standard form in the infinite time interval.

Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in by John Scott Russell (–) who observed a solitary wave in the Union Canal in Scotland.The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations.

It additionally develops the basics of control theory, which is a unique feature in current textbook literature. The following topics are particularly emphasised: • existence, uniqueness and continuation of solutions.

A2A: Linearity has a couple of very different mathematical meanings in different contexts. The most familiar case is an equation that graphs as a straight line. These typically have the form [math]y=ax+b[/math]. Mathematicians and scientists seldo.