Maric V. — Regular Variation and Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Maric V. — Regular Variation and Differential Equations

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Название: Regular Variation and Differential Equations

Автор: Maric V.

Аннотация:

This is the first book offering an application of regular variation to the qualitative theory of differential equations. The notion of regular variation, introduced by Karamata (1930), extended by several scientists, most significantly de Haan (1970), is a powerful tool in studying asymptotics in various branches of analysis and in probability theory. Here, some asymptotic properties (including non-oscillation) of solutions of second order linear and of some non-linear equations are proved by means of a new method that the well-developed theory of regular variation has yielded. A good graduate course both in real analysis and in differential equations suffices for understanding the book.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2000

Количество страниц: 127

Добавлена в каталог: 06.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abelian theorems      V
Ackerberg, R.C.      105 119
Aljancic, S.      119
Asymptotic inverse      99
Avakumovic, V.G., V      5 72 74 89 119
Balkema, A.A.      72
Bari, N.K.      5 119
Bekessy, A.      4 119
Bellman, R.      67 119
Bingham, N.H., V      119
Bojanic, R.      119
Cauchy principle      20
Cauchy — Schwartz inequality      60
Coppel, W.A.      56 119
De Haan, L., V      1 72 115 120
De Haan’s class      2 6
Differential equations of boundary layer theory      1 105
Differential equations of ferroelectrical phenomena      90
Differential equations, Airy      45
Differential equations, Emden — Fowler      72 89 101
Differential equations, Euler      14
Differential equations, Legendre      44
Differential equations, Poisson      71
Differential equations, Prandtl      105
Differential equations, Riccati      33
Differential equations, Schrodinger      1
Differential equations, second order linear      1 7 8 9
Differential equations, second order linear general      41
Differential equations, second order linear selfadjoint      43 45
Differential equations, second order nonlinear      1
Differential equations, Thomas-Fermi (atomic model)      71 89
Eastham, M.S.P.      119
Fedoryuk, M.V.      120
Feller, W., V      120
Fermi, E.      120
Fowler, R.H.      72 89
Functions of class $n^{2}$       46
Functions of class II      6 22 46 47 70
Functions of class r      6 22 64 65 118
Functions, almost decreasing      5 56 76 77 82 97 98 117
Functions, almost increasing      5 77 81 97 117
Functions, Beurling slowly varying      7 22 24 62 63 64 118
Functions, convex      75
Functions, logarithmico-exponential      7
Functions, rapidly varying      2 4 72 90 91 117
Functions, rapidly varying at zero      90 92
Functions, regularly bounded      2 5 76 81 117
Functions, regularly bounded at zero      76 82
Functions, regularly varying at zero      5 86 89 92 99 105
Functions, regularly varying, V      2 3 12 14 23 33 64 72 86 87 89 91 93 99 116 117
Functions, slowly varying      2 3 7 23 61 66 67 81 82 91 92 93 115 117
Functions, slowly varying at zero      82 93 115
Functions, slowly varying normalized      3 12 15 30 31 32 37 40 41 42 43 51
Functions, smoothly varying      72
Functions, superlinear      102
Geluk, J.L., V      22 46 70 72 74 120
Germs of real-valued functions      7
Goldie, C.M., V      119
Green, G.      1 120
Grimm, L.J.      43 120
Hacik, M.      62 70 120
Hall, L.H.      43 120
Hardy field      7
Hardy, G.H., V      7 121
Hartman, Ph.      55 56 70 121
Heading, J.      121
Hille’s criterion      27
Howard, H.C., V      121
Its, A.R.      69 121
Karamata class      1 2 5 12 21 26 27 91

Karamata, J., V      1 2 5 115 121
Kohlbecker, E.E.      3 121
Lebesgue dominated convergence theorem      30
Liouville Green approximation      45 67 69
Liouville, J.      1 122
Littlewood, J.L.      V
Marie, V.      12 75 91 120 121 122 123
Marik, J.      62 123
Marini, M.      10 123
Me Leod, J.B.      105 106 107 109 123
Mercerian theorems      V
Murray, J.D.      123
Nayfeh, A.H.      123
Nonstandard asymptotic analysis      114
Olwer, F.W.J.      123
Omey, E., V      12 22 46 62 70 120 123 124
Phase integral method      69
Potter’s criterion      46
Rab, M.      62 123
Radasin, Z.      91 106 121 122 123
Representation theorem      3 9 13 15 31 33 36 40 42 52
Representation theorem for regularly, bounded functions      40
Rosenlicht, M.      124
Sataric, M.V.      90 124
Seneta, E., V      124
Shemsidini, Z.Y.      124
Slavyanov, S.Yu.      124
Solutions of a boundary layer equation, existence of      105 107
Solutions of a boundary layer equation, regular boundedness of      105 113
Solutions of a boundary layer equation, regular variation and asymptotic behaviour of      105 113
Solutions of a boundary layer equation, uniqueness of      105 109
Solutions of equations of Thomas-Fermi type, regular boundedness of      76
Solutions of equations of Thomas-Fermi type, regular variation and asymptotic behaviour of      72 83
Solutions of equations of Thomas-Fermi type, slow variation and asymptotic behaviour of      83
Solutions of second order linear equations of class $\Gamma$       24
Solutions of second order linear equations of class $\Pi R_{2}$       21 46 47
Solutions of second order linear equations of class $\Pi$       22 23
Solutions of second order linear equations, nonoscillatory      8 26 27 28 30 43 46 68
Solutions of second order linear equations, nonprincipal      19
Solutions of second order linear equations, oscillatory      8 26 27 69
Solutions of second order linear equations, principal      19
Solutions of second order linear equations, rapidly varying; asymptotic behaviour of      69
Solutions of second order linear equations, rapidly varying; existence of      17 19 21 44 45
Solutions of second order linear equations, regularly bounded      26 40 68
Solutions of second order linear equations, regularly varying, existence of      12 14 19 21 26 27 32 41 42 43
Solutions of second order linear equations, regularly varying; asymptotic behaviour of      58 61 62
Solutions of second order linear equations, slowly varying; asymptotic behaviour of      49 51 52 54
Solutions of second order linear equations, slowly varying; existence of      12 19 21 30
Solutions of second order linear equations, zeros of      62 63 64
Steckin, S.B.      5 119
Stirling’s formula      100
Sturm separation theorem      26
Successive approximations method      28 34 38 50
Swanson, C.A.      124
Taliaferro, S.      74 91 102 104 124
Tauberian theorems, V      72
Teugels, J.L., V      119
Thomas, L.H.      124
Tomic, M., V      12 26 75 119 120 122
Tuszynski, J.A.      124
Uniform convergence theorem      3
Van der Berg, J.P.      114 119
Wiener, N.      V
Willekens, E.      46 124
Willett, D.      124
Wintner, A.      55 56 70
WKBJ method      69
Wong, P.K.      74 82 124
Wronski, H.      9 10
Zakula, R.B.      124
Zezza, P.      10 123

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