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Bailey P.B. — Nonlinear Two Point Boundary Value Problems
Bailey P.B. — Nonlinear Two Point Boundary Value Problems



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Название: Nonlinear Two Point Boundary Value Problems

Автор: Bailey P.B.

Аннотация:

The purpose of this book is to describe as simply as possible a number of the ideas and methods which seem to be particularly helpful in the study of nonlinear boundary value problems for differential equations of the second order. Apart from the restriction to second order, the kinds of equations treated and the level of treatment are those common to introductory courses in differential equations which treat initial value problems. The reason for this restriction is that whereas nth order initial value problems are not essentially more difficult than first or second order, higher order boundary value problems are. Those of second order already show the difficulties but are becoming fairly well understood. Much of the material has only recently appeared in the mathematical literature, however, and cannot yet be found in the textbooks.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 171

Добавлена в каталог: 10.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha(L, K)$, definition of      59
$\beta(L, K)$, definition of      60
Akilov, G.P.      166
Babkin, B.N.      101
Bailey, P.      68 99 100 126
Bebernes, J.W.      127
Beckenbach, E.F.      86
Bellman, R.      86 139 166
Bertolino, M.      86
Bessel's equation      66—68
Birkhoff, G.      47
Bisshopp, K.E.      87
Bounding curves      96 119 132
Cantilever beam      83—85
Caplygin, S.A.      86
Cauchy sequence      25
Cinquini, S.      101
Coddington, E.A.      15 69
Coffman, C.V.      15
Coles, W.J.      47 68
Collatz, L.      47 48 87 127 140 165
Comparison theorems      70—87
Comparison theorems for strong inequalities      73
Comparison theorems for weak inequalities      80
Continuability      see "Initial value problem"
Contraction mapping      25
Contraction mapping, error bound      26 38
Contraction mapping, principle of      26 42
Corresponding solutions      71
Courant, R.      47
de la Vallee Poussin, C      68
Defect      148
Dependence of solutions on initial conditions and parameters      11
Differential inequalities      55 71 104 see
Discrete boundary value problem      157
Distance between zeros      50—61
Distance between zeros, explicit bounds      59—60
Drucker, D.C.      87
Ehrmann, H.      48 101 102 126
Epheser, H.      101
Error bound for Picard iterates      26 38
Existence theorems, principal, discrete boundary value problem      157
Existence theorems, principal, first boundary value problem      12 20 37 96 108 114
Existence theorems, principal, infinite interval boundary value problems      110—111
Existence theorems, principal, initial value problem      10
Existence theorems, principal, second boundary value problem      35—36 93 108 111
Finite difference method      156
First boundary value problem, defined      3
First boundary value problem, existence, principal theorems      12 20 37 96 108 114
First boundary value problem, uniqueness, principal theorems      18 20 37 61 113
Fountain, L.      86 101
Fox, L.      165 167
Gas flow example      122
Green's function for modified Picard's iteration      151
Green's function for Picard's iteration      22—23
Gross, O.A.      127
Hammerstein, A.      15
Hartman, P.      15 48
Hartree, D.R.      140
Henrici, P.      140 166 167
Hilbert, D.      47
Hurewicz, W.      15
Infinite interval boundary value problems      110—111 120 122 133 137
Initial value problem, continuability      10
Initial value problem, continuous dependence on initial conditions      11
Initial value problem, defined      2
Initial value problem, existence of solution      10
Initial value problem, uniqueness of solution      10
Integral equations, formulation as      22—24
Jackson, L.      86 101 127
Kalaba, R.      166
Kamke, E.      48
Kantorovich, L.V.      166
Keller, H.B.      102 140
Kidder, R.E.      127
Knobloch, H.-W.      86
Kolodner, I.I.      15
Lasota, A.      15 68
Lees, M.      102
Lettenmeyer, F.      47 68
Levinson, N.      15 69
Lipschitz condition      1—5
Lipschitz condition, defined      1
Lipschitz condition, generalized      3—5 103 110
Lipschitz constants defined      1 4
Love, A.H.      69
Milne, W.E.      140
Monotone iteration      147—153
Moroney, R.M.      15
Moyer, R.D.      102
Nagumo, M.      100 101 126
Nehari, Z.      16
Newton's method      144 153—156
Nonnegative solutions      116
Norms, change of      29 34
Norms, equivalence of      31
Numerical solution of boundary value problems      128—167
Numerical solution of boundary value problems, boundary value methods      141—167
Numerical solution of boundary value problems, initial value methods      128—140
Opial, Z.      15 68
Parter, S.V.      16
Peixoto, M.M.      86
Pendulum, differential equation of      13 64 99 102
Pereyra, V.      167
Petry, W.      48 68 126
Picard's iteration      21—49 see
Picard's iteration, denned      21 27
Picard's iteration, modified      144
Picard's iteration, use in computation      143
Picard, E.      14 21 47 48
Pimbley, G.H., Jr.      16
Reduction to zero boundary conditions      23
Rota, G.-C      47
Rudin, W.      166
Schroeder, J.      47 48 87 166
Scorza Dragoni, G.      100
Second boundary value problem      3
Second boundary value problem, existence, principal theorems      35—36 93 108 111
Second boundary value problem, uniqueness, principal theorems      35 61 113
Shampine, L.F.      99 100 126
Sherman, T.L.      47 68
Shooting method      128—140
Shooting method, convergence of      130
Singular boundary value problems      110—112
Slugin, S.      166
Stetter, H.J.      167
Successive approximation      see "Picard's iteration" "Contraction
Szarski, J.      86
Todd, J.      166
Tonelli, L.      100
Tricomi, F.G.      102
Unforced equations      51
Unforced equations, distance between zeros      54—63
Uniqueness and unforced equations      52
Uniqueness theorems, principal, first boundary value problem      18 20 37 61 113
Uniqueness theorems, principal, infinite interval boundary value problems      110—111
Uniqueness theorems, principal, initial value problem      10
Uniqueness theorems, principal, second boundary value problem      35 61 113
Unstable initial value problems      141
Waltman, P.      68 99 100 126
Weight functions      29 34 48
Weissinger, J.      48
Wilkins, J.E., Jr.      86
Zero boundary conditions, reduction to      23
Zeros, distance between      59—60
Zwirner, G.      100
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