Nevalinna Theory and Complex Differential Equations

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Shows how the Nevanlinna theory may be applied to gain insight into complex differential equations. Chapter topics include results from function theory; the Nevanlinna theory of meromorphic functions; Wilman-Valiron theory; linear differential equations with zero distribution in the second order case; complex differential equations and the Schwarzian derivative; Malmquist- Yosida-Steinmetz type theorems; first order, second order, and arbitrary order algebraic differential equations; and differential fields. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Introduction 1
Ch. 1 Results from function theory 5
Ch. 2 Nevanlinna theory of meromorphic functions 18
Ch. 3 Wiman-Valiron theory 50
Ch. 4 Linear differential equations: basic results 53
Ch. 5 Linear differential equations: zero distribution in the second order case 74
Ch. 6 Complex differential equations and the Schwarzian derivative 110
Ch. 7 Higher order linear differential equations 127
Ch. 8 Non-homogeneous linear differential equations 144
Ch. 9 Basic non-linear differential equations 165
Ch. 10 The Malmquist-Yosida-Steinmetz type theorems 192
Ch. 11 First order algebraic differential equations 221
Ch. 12 Second order algebraic differential equations 248
Ch. 13 Algebraic differential equations of arbitrary order 257
Ch. 14 Algebraic differential equations and differential fields 285
Bibliography 311
Index 339
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