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Heikkila S., Lakshmikantham V. — Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations
Heikkila S., Lakshmikantham V. — Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations



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Название: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

Авторы: Heikkila S., Lakshmikantham V.

Аннотация:

Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 514

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l^p$-space of real sequences      49
$L^p$-space of real valued functions      48
$l^p$-space of vector sequences      480
$L^p$-space of vector valued functions      465
Almost everywhere (a.e.)      36
Axiom of Choice      6
Axiom, schema of replacement      8
Banach space, ordered      30
Banach space, reflexive      30
Boundary value problem, (BVP), elliptic      285
Boundary value problem, quaslinear elliptic      267
Boundary value problem, second order      218
Boundary value problem, second order, mixed monotone      233
Caratheodory      69 419
Chain      3
Compact      17
Compact, relatively      17
Compact, sequentially      18
Cone, fully regular      28
Cone, normal      28
Cone, order      27
Cone, positive      27
Cone, regular      27
Cone, strongly minihedral      546
Convergence      16
Convergence, strong      28
Convergence, weak      30 463
Cosine family, strongly continuous      435
Coupled quasisolutions of ellitpic BVP system      298
Coupled quasisolutions of finite scalar, BVP system      256
Coupled quasisolutions of finite scale, IVP system      152
Coupled quasisolutions of finite scale, PBVP system      173
Coupled quasisolutions of first order IVP in Banach space      394
Coupled quasisolutions of first order PBVP in Banach space      398
Coupled quasisolutions of infinite scalar, PBVP system      213
Coupled quasisolutions of scalar BVP      234
Coupled quasisolutions of scalar IVP      107
Coupled quasisolutions of scalar PBVP      131
Coupled quasisolutions of second order PBVP in Banach space      406
Coupled quasisolutions of second order, IVP in Banach space      402
Dependence on initial data of IVP in Banach space      334
Dependence on initial data, first order infinite scalar IVP system      187
Dependence on initial data, first order scalar IVP system      143
Dependence on initial data, first order semilinear IVP in Banach space      359 428
Dependence on initial data, first order, scalar IVP      95
Dependence on initial data, higher order IVP in Banach space      373
Dependence on initial data, second order, semilinear IVP in Banach space      450
Dependence on initial values: of first order IVP, IVP in Banach space      334
Dependence on initial values: of first order semilinear, IVP in Banach space      354 417
Dependence on initial values: of higher order IVP in Banach space      369
Dependence on initial values: of second order semilinear IVP in Banach space      439
Derivative      51
Dirichlet boundary conditions      285
Dominated Convergence Theorem      4
Dual space      267
Duality pairing      267
Element, greatest      3
Element, least      3
Element, maximal      3
Embedding, compact      304
Embedding, continuous      31
Equicontinuous      33
Essential supremum      48
Extremal coupled quasisolutions of elliptic BVP system      299
Extremal coupled quasisolutions of finite BVP system      256
Extremal coupled quasisolutions of finite scalar, IVP system      153
Extremal coupled quasisolutions of finite scalar, PBVP system      175
Extremal quasisolutions of first order IVP in Banach space      394
Extremal quasisolutions of first order PBVP in Banach space      398
Extremal quasisolutions of first order, scalar IVP      110
Extremal quasisolutions of infinite scalar, PBVP system      215
Extremal quasisolutions of parabolic IBVP system      326
Extremal quasisolutions of scalar BVP      234
Extremal quasisolutions of scalar PBVP      133
Extremal quasisolutions of second order order, IVP in Banach space      402
Extremal quasisolutions of second order, order PBVP in Banach space      412
Extremal solutions of elliptic BVP      287
Extremal solutions of elliptic BVP system      294
Extremal solutions of first order IVP in Banach space      341
Extremal solutions of first order IVP system in Banach space      370
Extremal solutions of first order PBVP in Banach space      380
Extremal solutions of first order semilinear IVP in Banach space      350
Extremal solutions of first order, finite IVP system      135
Extremal solutions of first order, finite PBVP system      164
Extremal solutions of first order, infinite IVP system      177
Extremal solutions of first order, infinite PBVP system      204
Extremal solutions of first order, scalar IVP      68 86
Extremal solutions of first order, scalar PBVP      121
Extremal solutions of higher order IVP in Banach space      370
Extremal solutions of higher order, scalar IVP      151
Extremal solutions of parabolic IBVP      316
Extremal solutions of parabolic, IBVP system      324
Extremal solutions of quasilinear, elliptic BVP      278
Extremal solutions of second order BVP      225
Extremal solutions of second order PBVP in Banach space      392
Extremal solutions of second order, finite BVP system      241
Extremal solutions of second order, infinite BVP system      248
Finite intersection property      17
Finite systems of first order IVP’s      134 152
Finite systems of first order PBVP’s      164
Finite systems of second order BVP’s      240 255
Finite systems of second order, elliptic BVP’s      292 298
Finite systems of second order, parabolic IBVP’s      321
Fixed point of mapping      7
Fixed point of multifunction      6
Fixed point, coupled      24
Fixed point, extremal      21
Fixed point, extremal coupled      24
Fixed point, greatest      21
Fixed point, least      21
Fixed point, unique      66
Form, bilinear      285
Form, semilinear      268
Function of strong bounded variation      51
Function, $\mu$-integrable      37
Function, a.e. differentiable      52
Function, absolutely continuous      51
Function, almost left regulated      42
Function, almost right regulated      42
Function, Bochner integrable      38
Function, Borel measurable      47
Function, bounded      37
Function, Caratheodory      46
Function, conjugate      473
Function, countably stepped      38
Function, differentiable      51
Function, Dirichlet      42
Function, essentially bounded      37
Function, Heaviside      281
Function, Lebesgue integrable      38
Function, left regulated      38
Function, Lipschitz continuous      51
Function, measurable      38
Function, monotone      20
Function, N-      472
Function, nondecreasing      20
Function, nonincreasing      20
Function, quasimonotone      134
Function, quasimonotone nonincreasing      134
Function, quasimonotone, nondecreasing      134 338
Function, regulated      38
Function, right regulated      38
Function, standard      47
Function, step      36
Function, stepped      38
Function, strongly measurable      37
Functional, linear      30
Generalized      474
Gronwall’s lemma, generalized      81
Hilbert space      458
Hilbert space, ordered      458
Holder’s Inequality      466
Infimum      3
Infinite systems of first order, IVP’s      175 193
Infinite systems of first order, PBVP’s      204
Infinite systems of second order, BVP’s      247 261
Infinitesimal generator      435
Initial value problem (IVP), first order differential equation      67 85 331
Initial value problem (IVP), first order partial differential equation      429
Initial value problem (IVP), first order semilinear differential equation      350 415
Initial value problem (IVP), higher order diffential equation      149 366
Initial value problem (IVP), second order hyperbolic differential equation      451
Initial value problem (IVP), second order parabolic differential equation      433
Initial value problem (IVP), second order semilinear differential equation      434
Initial-boundary value, problem (IBVP)      303
Integrability, Bochner      38
Integrability, Lebesgue      38
Integrability, Riemann      40
Inversely well-ordered (i.w.o)      3
Inversely well-ordered (i.w.o), chain of iterations      22
Lattice      3
Least upper bound      3
left-hand      51
Leray — Lions conditions      268 304
Limit, weak      463
Lipschitz boundary      267
Lipschitz condition, generalized      221 337
Lower bound      3
Lower bound, strict      3
Mapping, linear      47
Mapping, mixed monotone      24
Mapping, monotone      20
Mapping, nondecreasing      20
Mapping, nonincreasing      20
Mapping, order bounded      24
Mapping, order-preserving      350
Mapping, truncation      271 307
Maximal or minimal solution of first order IVP in Banach space      356 426
Maximal or minimal solution of higher order, IVP in Banach space      372
Maximal or minimal solution of second order semilinear, IVP in Banach space      447
Mazur’s theorem      46
Measure, $\sigma$-finite      479
Measure, counting      49
Measure, finite      36
Measure, Lebesgue      37
Measure, positive      36
Measure, space      36
Metric space, complete      40
Metric space, ordered      18
Minimum      3
Nagumo condition      221
Norm in $l^p$      49
Norm in $l^p(E)$      480
Norm in $L^p(\Omega)$      48
Norm in $L^p(\Omega,E)$      465 468
Norm in Luxemburg      473
Norm in Orlicz — Sobolev space      475
Norm in semimonotone      28
Norm in Sobolev space      475
Norm in space ($c_0$)      57
Norm in space of cont. functions      58
Norm in strictly monotone      456
Norm in uniformly monotone      456
Normed space, complete      30
Normed space, ordered      28
Normed space, weakly complete      465
Null set      36
Operator, coercive      274 309
Operator, Leray — Lions      273
Operator, maximal monotone      309
Operator, pseudomonotone      273
Operator, superposition      44 271 308
Operator, uniformly elliptic      285
Order interval      3
Ordering, partial      2
Ordering, strict      2
Orlicz space      472
Orlicz — Sobolev space      475
Partial differential equation, elliptic      285
Partial differential equation, elliptic system      292
Partial differential equation, first order      429
Partial differential equation, hyperbolic      451
Partial differential equation, parabolic      303 433
Partial differential equation, parabolic system      321
Periodic boundary value problem (PBVP), first order      76 121 380
Periodic boundary value problem (PBVP), mixed monotone      398 406
Periodic boundary value problem (PBVP), second order      386
POSET      2
Relation, antisymmetric      2
Relation, irreflexive      2
Relation, reflexive      2
Relation, transitive      2
right-hand      51
Semigroup, strongly continuous      452
Sequence, approximating      37
Sequence, bounded      28
Sequence, cluster point of      15
Sequence, decreasing      3
Sequence, increasing      3
Sequence, monotone      4
Sequence, nondecreasing      3
Sequence, noninreasing      3
Sequence, order bounded      28
Sequence, transfinite      7
Set, Borel      47
Set, bounded      18
Set, closure      15
Set, cofinal      3
Set, countable      3
Set, directed      3
Set, Lebesgue measurable      37
Set, measurable      36
Set, order bounded      3
Set, separable      17
Sine family, strongly continuous      435
Sobolev space      267 474
Solution of elliptic BVP      286
Solution of elliptic BVP system      292
Solution of first order scalar IVP      68
Solution of higher order IVP in Banach space      367
Solution of higher order scalar IVP      149
Solution of parabolic IBVP      305
Solution of parabolic IBVP system      322
Solution of quasilinear elliptic BVP      268
Solution of second order BVP      218
Solution, extremal      see “Extremal solutions”
Solution, extremal mild      421 442
Solution, lower      68 218 269 286 293 305 322
Solution, lower mild      421 442
Solution, maximal      68
Solution, mild      416 430 433 442 451
Solution, minimal      68
Solution, strong      435
Solution, upper      68 218 268 286 293 305 322
Solution, upper mild      421 442
Solution, weak      436
Space ($c_0$)      57
Space of bounded functions, ordered      476
Space of continuous functions, ordered      33 58 478
strong      51
Supremum      3
Topological space, first countable      17
Topological space, ordered      15
UMB-space      456
Uniqueness of solution of first order IVP in Banach space      331
Uniqueness of solution of first order scalar IVP      73
Uniqueness of solution of first order scalar PBVP      77
Uniqueness of solution of first order semilinear, IVP in Banach space      354 416
Uniqueness of solution of higher order IVP in Banach space      368
Uniqueness of solution of second order BVP      220
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