Agarwal R.P., O'Regan D., Grace S.R. — Oscillation Theory for Second Order Linear, Half-Linear :: Электронная библиотека попечительского совета мехмата МГУ

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Agarwal R.P., O'Regan D., Grace S.R. — Oscillation Theory for Second Order Linear, Half-Linear

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Название: Oscillation Theory for Second Order Linear, Half-Linear

Авторы: Agarwal R.P., O'Regan D., Grace S.R.

Аннотация:

Agarwal (Florida Institute of Technology), Grace (Cairo University) and O'Regan (University of Ireland) develop oscillation and non- oscillation theory for second order differential equations, with separate chapters addressing the solution of linear, half-linear, superlinear, and sublinear types of equations. Suitable for use as a graduate text, the book also discusses the oscillatory behavior of nonlinear two-dimensional differential systems and second order vector-matrix differential equations, and examines the behavioral properties of solutions of differential equations near infinity

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2002

Количество страниц: 692

Добавлена в каталог: 17.04.2008

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Предметный указатель

Arzela — Ascoli theorem      11
Asymptotic behavior      549 559 562 567 589 608
Averaging technique      40
Banach lattice      540
Besicovitch seminorm      107
Besieovitch almost periodic functions      107
Bounded solution      4—6 8 10 562
Compactness criterion      11 657
Comparison theorems      15
conjugate      469
Continuability      2
Converges to zero      6—8 10
Damped equation      205 376
Decaying nonoscillatory solution      262
Differential inclusion      656 657
Differential system      503
Differential system with forcing term      549
Disconjugate      467 504
Distance of zeros      210
Emden — Fowler equation      36 433 457 493 641
Euler differential equation      17 23 38 69
Euler — Lagrange equation      94
Fitzpatrick — Petryshyn fixed point theorem      657
Forced equation      82 205 632
Functional differential equations      218 237
Functionally commutative      533
General damped equation      274
Generalized Emden — Fowler equation      559
Generalized Euler equation      467
Generalized Pruefer transform      164
Generalized Riccati equation      209 467 470
Generalized sine function      164
Gronwall inequality      2
Half-linear differential equation      94 444 466 552
Hartman's oscillation criterion      90
Hille theorem      601
Hille — Wintner comparison theorem      332 540
Integrably small      70
Integral averaging technique      168
Interval criteria      179
Interval oscillation      64 66
Kummer transformation      90
Ky-Fan fixed point theorem      656
Lebesgue dominated convergence theorem      11
Left disfocal      213
Leighton's oscillation criterion      90
Levin-type comparison theorem      100
Liapunov function      477
Liapunov inequality      105
Liapunov second method      476
Limit circle type      639

Limit point type      639
Linearization result      339 429
Maximal solution      342 636 637
Minimal solution      342 636 637
Mixed type equation      257
Neutral equation      233
Neutral inclusions      656 664
Nonlinear damping term      362
Nonoscillatory      1 492
Nonoscillatory characterization      15
Nonprincipal Solution      467
Olech — Opial — Wazewski method      457
Operator-valued differential equation      540
Oscillatory      1 492 504
Picone identity      14
Positive decaying solution      595
Positive increasing solution      608
Positive solution      585 614
Prepared solution      504
Principal solution      467
Proper solution      113 585
Quickly oscillatory      107
Riccati differential equation      501
Riccati inequality      506
Riccati integral equation      22 501 505
Riccati transformation      466
Riccati variable      544
Right disfocal      213
Right hand derivative      477
Schauder fixed point theorem      11
Schauder — Tychonov fixed point, theorem      11
Self-conjugate      504
Singular Emden — Fowler equation      584 602 006
Singular Emden — Fowler system      614 620
Solution      1 4
Strongly sublinear      448
Strongly superlinear      274
Sturm theorem      13 94 99 620
Sturm — Picone theorem      15 625 628
Sturmian identity      14
Sublinear      376 377 433 498 569
Superlinear      274 296 493 566
Superlinear forced equation      358
Two-dimensional differential system      492
Unforced equation      82
Variational Principle      467
Weighted function      46
Weighted-average oscillation criteria      188
Weighted-integral condition      45
Willett's oscillation criterion      90
Wirtinger type inequality      96
wronskian      14

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