Meromorphic Solutions of Some Composite Functional Equations
Author | : Heli Silvennoinen |
Publisher | : |
Total Pages | : 46 |
Release | : 2003 |
Genre | : Functional equations |
ISBN | : |
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Author | : Heli Silvennoinen |
Publisher | : |
Total Pages | : 46 |
Release | : 2003 |
Genre | : Functional equations |
ISBN | : |
Author | : J. Aczel |
Publisher | : Courier Corporation |
Total Pages | : 548 |
Release | : 2006-02-01 |
Genre | : Mathematics |
ISBN | : 0486445232 |
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Author | : Kwok-Kin Wong |
Publisher | : Open Dissertation Press |
Total Pages | : |
Release | : 2017-01-26 |
Genre | : |
ISBN | : 9781361281901 |
This dissertation, "Exact Meromorphic Solutions of Complex Algebraic Differential Equations" by Kwok-kin, Wong, 黃國堅, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: For any given complex algebraic ordinary differential equation (ODE), one major task of both pure and applied mathematicians is to find explicit meromorphic solutions due to their extensive applications in science. In 2010, Conte and Ng in [12] proposed a new technique for solving complex algebraic ODEs. The method consists of an idea due to Eremenko in [20] and the subequation method of Conte and Musette, which was first proposed in [9]. Eremenko's idea is to make use of the Nevanlinna theory to analyze the value distribution and growth rate of the solutions, from which one would be able to show that in some cases, all the meromorphic solutions of the studied differential equation are in a class of functions called "class W," which consists of elliptic functions and their degenerates. The establishment of solutions is then achieved by the subequation method. The main idea is to build subequations which have solutions that also satisfy the original differential equation, hoping that the subequations will be easier to solve. As in [12], the technique has been proven to be very successful in obtaining explicit particular meromorphic solutions as well as giving complete classification of meromorphic solutions. In this thesis, the necessary theoretical background, including the Nevanlinna theory and the subequation method, will be developed. The technique will then be applied to obtain all meromorphic stationary wave solutions of the real cubic Swift-Hohenberg equation (RCSH). This last part is joint work with Conte and Ng and will appear in Studies in Applied Mathematics [13]. RCSH is important in several studies in physics and engineering problems. For instance, RCSH is used as modeling equation for Rayleigh- B?nard convection in hydrodynamics [43] as well as in pattern formation [16]. Among the explicit stationary wave solutions obtained by the technique used in this thesis, one of them appears to be new and could be written down as a rational function composite with Weierstrass elliptic function. DOI: 10.5353/th_b4833021 Subjects: Differential-algebraic equations
Author | : Sui Sun Cheng |
Publisher | : World Scientific |
Total Pages | : 296 |
Release | : 2008-03-14 |
Genre | : Mathematics |
ISBN | : 9814471720 |
This book presents a self-contained and unified introduction to the properties of analytic functions. Based on recent research results, it provides many examples of functional equations to show how analytic solutions can be found.Unlike in other books, analytic functions are treated here as those generated by sequences with positive radii of convergence. By developing operational means for handling sequences, functional equations can then be transformed into recurrence relations or difference equations in a straightforward manner. Their solutions can also be found either by qualitative means or by computation. The subsequent formal power series function can then be asserted as a true solution once convergence is established by various convergence tests and majorization techniques. Functional equations in this book may also be functional differential equations or iterative equations, which are different from the differential equations studied in standard textbooks since composition of known or unknown functions are involved.
Author | : Christopher G. Small |
Publisher | : Springer Science & Business Media |
Total Pages | : 139 |
Release | : 2007-04-03 |
Genre | : Mathematics |
ISBN | : 0387489010 |
Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.
Author | : Yanpei Liu |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 302 |
Release | : 2019-10-21 |
Genre | : Mathematics |
ISBN | : 3110625830 |
This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The first volume mainly presents basic concepts and the theoretical background. Differential (ordinary and partial) equations and relevant topics are discussed in detail.
Author | : Themistocles RASSIAS |
Publisher | : Springer Science & Business Media |
Total Pages | : 221 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 940170225X |
Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.