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Zhang B. G., Yong Z. — Qualitative analysis of delay partial difference equations
Zhang B. G., Yong  Z. — Qualitative analysis of delay partial difference equations

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Название: Qualitative analysis of delay partial difference equations

Авторы: Zhang B. G., Yong Z.

Аннотация:

Delay partial difference equations occur frequently in the approximation of solutions of delay partial differential equations by finite difference methods, random walk problems, the study of molecular orbits and mathematical physics problems. Many results have been done for the qualitative theory of delay partial difference equation in the past ten years. But there has not been a book in the literature presenting the systematical theory on delay partial difference equations so far. This book provides a broad scenario of the qualitative theory of delay partial difference equations.

The book is divided into five chapters. Chapter 1 introduces delay partial difference equations and related initial value problems, and offers several examples for motivation. In Chapter 2, we first discuss the oscillation of the linear delay partial difference equations with constants parameters, where the characteristic equations play an important rule; then we present some techniques for the investigation of the oscillation of the linear delay partial difference equations with variable coefficients. Chapter 3 is devoted to the study of the oscillation of the nonlinear delay partial difference equations. In Chapter 4, we consider the stability of the delay partial difference equations. In the last Chapter, we introduce some recent work on spatial chaos.

Most of the materials in this book are based on the research work carried out by authors, their graduate students and some other experts during the past ten years. Readership: Advanced undergraduates, graduates and researchers in applied mathematics, computation mathematics, physical and biological sciences.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 375

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^{2}$ stable      315
Allowable point      235
Asymptotic stability      253
Attractivity      247 252 315
Banach fixed point theorem      7
Boundary      235 321
Boundary, conditions      314
Boundary, value problem      237
Brouwer fixed point theorem      7
Cantor sets      348
Chaotic in the sense, Devaney      339 340 343 361
Chaotic in the sense, Li and Yorke      335 354 361
Characteristic equation      10 13 15 17
Comparison theorem      140 146
Complete metric space      331
Concave boundary point      235
Cone      7
Continuous argument      17
Continuous map      331
Contraction mapping theorem      7
Convection equation      332
Convex boundary point      236
Convex connected solid net      235
D-B-exponentially stable      290 293
Darbo fixed point theorem      282
Delay 2D discrete logistic equation      289 300
Delay parabolic equation      3
Delay partial difference equation      2
Delay reaction diffusion equation      1
Dense periodic points      338
Derived set      80
Difference inequality      42 73 111
Discrete dynamical system      331 337
Discrete Gaussian formula      235
Discrete Laplace operator      236
Discrete logistic system      289
Distance between two points      344
Distance between two sets      344
Equation with constant parameters      9 14
Equation with continuous arguments      17 72 152 270
Equation with oscillatory coefficients      63
Equation with positive and negative coefficients      107
Equation with several delays      20 56
Equation with unbounded delay      93
Equation with variable coefficients      21 139
Equation, Nicholson blowflies      220
Equilibrium point      302
Eventually negative      9 17
Eventually positive      9 17
Existence of oscillatory solutions      139 180
Existence of positive solutions      119 124 191
Expanding fixed point      344
Fabry theorem      6
Fixed point      282 302
Fixed point theorems      8
Frequency measure      80
Frequent oscillation      80
Frequently oscillatory of upper (lower) degree      81 88 91
Frequently positive (negative) of upper (lower) degree      81
Global attractivity      224 247
Heteroclinic point      346
Homeomorphic      345
Homoclinic orbit      347
Homoclinic point      346
Hyperbolic equation      13 241
Infinite-dimensional discrete dynamical system      337
Initial boundary value problem      2 226 235
Initial function      3
Initial value problem      2
Jensen integral inequality      154
Jensens inequality      7
Knaster — Tarski fixed point theorem      7
Krasnoselskii's fixed point theorem      7
Laplace transformation      5
Lattice point      80
Li — Yorke theorem      335
Liapunov function      253 271
Limiting equation      56 63
Linearized oscillation      139 146
Linearly stable      253 255 266
Local unstable set      346
Lower frequency measure      80
Maximum principle      326
Metric space      331
Monotone solution      112
Multidimensional IBVPs      139
Neutral partial difference equation      135
Nondegenerate snap-back repeller      345
Nonexistence of monotone solution      112
Nonlinear equation      139
Nonoscilltory solution      14
Oscillation      9 14
Parabolic equation      237
Parabolic Volterra difference equation      314 320
Partial delay survival red blood cells model      224
Partially ordered      7
Periodic orbit      331 347
Periodic point      332 349
Population model      220
Proper solution      10 14 17
Rectangular solid net      235
Regular expanding fixed point      346
Repeller      344
Sawtooth function      361
Schauder's fixed point theorem      7 213
Scrambled set      335
Sensitive dependence on initial conditions      338
Singular expanding fixed point      346
Snap-back repeller      344 345
Spatial chaos      331
Spatial orbits      331
Spatial periodic orbits      331
Stable      252 253 255
Stable, asymptotically      258 261
Stable, exponentially asymptotically      253 257 264 265 271
Stable, strongly exponentially asymptotically      253 265
Sublinear equation      173
Sublinear measure of noncompactness      283
Superlinear equation      175
Symbolic dynamical system      348
System of partial difference equations      281
Topologically conjugate      350
Totally disconnected      348
Transitivity      338
Translation operator      80
Triangle graphical method      247
Unbounded delay      93
Unbounded solution      150
Uniformly Cauchy      181
Unstable      267 270 279
Upper frequency measure      80
Vandermonde determinant      334
Volterra difference equations with diffusion and infinite delay      320
Z-transformation      4
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