ISBN: 3-540-67160-9
TITLE: Regular Variation and Differential Equations
AUTHOR: Maric, Vojislav
TOC:

Introduction 1
Part One. Linear Equations 9
Chapter 1. Existence of regular solutions 9
1.1. Preliminaries 9
1.2. The case f(x) < 0 12
1.3. Pi- and Gamma- varying solutions 21
1.4. The case of f(x) of arbitrary sign 26
1.5. Regular boundedness of solutions 40
1.6. Generalizations 41
1.7. Examples 44
1.8. Comments 46
Chapter 2. Asymptotic behavior of regular solutions 49
2.1. Slowly varying solutions 49
2.1. a)The case of f(x) of arbitrary sign 49
2.2. Regularly varying solutions 57
2.3. On zeros of oscillating solutions 62
2.4. Examples 65
2.5. Comments 70
Part Two. Nonlinear Equations 71
Chapter 3. Equations of Thomas-Fermi type 71
3.1. Introduction and preliminaries 71
3.2. The case of regularly varying f and theta 75
3.3. Examples 89
3.4. The case of rapidly varying f or theta 90
3.5. Examples 99
3.6. A more general case 102
Chapter 4. An equation arising in boundary-layer Theory 105
4.1. Introduction 105
4.2. Existence and uniqueness 106
4.3. Estimates and asymptotic behavior of solutions 109
4.4. Comments 114
Appendix. Properties of Regularly Varying and Related Functions 115
References 119
Index 125
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