Hillis equation Hill方程
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内容提要：
This two-part treatment of Hill's equation encompasses the subject's most pertinent information, explaining both basic theory and numerous details, including elementary formulas, oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention is given to stability problems and the question of coexistence of periodic solutions. 1966 edition.
目录：
PART Ⅰ GENERAL THEORY
Ⅰ Basic Concepts 1.1 Preliminary Remarks 1.2 Floquet's Theorem 1.3 The Symmetric Case Q(x) = Q(-x) Ⅱ Characteristic Values and Discriminant 2.1 Characteristic Values and Intervals of Stability 2.2 Analytic Properties of the Discriminant 2.3 Infinite Determinants 2.4 Asymptotic Behavior of the Characteristic Values 2.5 Basic Results from the general Theory of Linear Differential Eqtiations 2.6 Theorems of Liapounoff and Borg. Fourier Transforms PART Ⅱ. DETAILS Ⅲ Elementary Formulas 3.1 Transformation into aStandard Form 3.2 The Liouville Transformation 3.3 Polar Coordinates 3.4 Differential Equation for the Product of Two Solutions Ⅲ Oscillatory Solutions Ⅴ Intervals of Stability and Instability 5.1 Introduction 5.2 Regions of Absolute Stability 5.3 Equations with Two or More Parameters 5.4 Remarks on a Perturbation Method 5.5 Applications of the Theory of Systems of Differential Equations 5.6 The Instability Intervals Ⅵ Discriminant Ⅶ Coexistence 7.1 Introduction 7.2 Ince's Equation 7.3 Lame's Equation and Generalizations 7.4 The Whittaker-Hill Equation 7.5 Finite Hill's Equations 7.6 Extreme Cases of Coexistence Ⅷ Examples 8.1 Impulse Functions 8.2 Piecewise Constant Functions 8.3 Piecewise Linear Functions 8.4 The Frequency Modulation Equation List of Symbols and Notations List of Theorems, Lemmas, and Corollaries References Additional References Index |