Introduction to the theory and applications of functional differential equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1999
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| Series: | Mathematics and its applications
463 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 648 S. graph. Darst. |
| ISBN: | 0792355040 |
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| adam_text | INTRODUCTION TO THE THEORY AND APPLICATIONS OF FUNCTIONAL DIFFERENTIAL
EQUATIONS BY V. KOLMANOVSKII MOSCOW STATE UNIVERSITY OF ELECTRONICS AND
MATHEMATICS AND SPACE RESEARCH INSTITUTE (1KI) OF THE RUSSIAN ACADEMY OF
SCIENCES, MOSCOW, RUSSIA AND A. MYSHKIS MOSCOW STATE UNIVERSITY OF
COMMUNICATIONS (MIIT), MOSCOW, RUSSIA KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON PREFACE CONTENTS I PART I. MODELLING BY
FUNCTIONAL DIFFERENTIAL EQUATIONS CHAPTER 1. THEORETICAL PRELIMINARIES
11 1. FUNCTIONAL DIFFERENTIAL EQUATIONS (FDES) 11 1.1 SOME CLASSES OF
FDES 11 1.2 SOLUTION CONCEPT FOR A FDE 12 1.3 FDE WITH RETARDATION 14
1.4 A LITTLE BIT OF PHILOSOPHY 19 CHAPTER 2. MODELS 23 1.
VISCOELASTICITV 23 2. AFTEREFFECT IN MECHANICS 25 2.1 MOTION OF A
PARTICLE IN A LIQUID 25 2.2 CONTROLLED MOTION OF A RIGID BODY 26 2.3
MODELS OF POLYMER CRYSTALLIZATION 28 2.4 STRETCHING OF A POLYMER
FILAMENT 28 3. HEREDITARY PHENOMENA IN PHYSICS 30 3.1 DYNAMICS OF
OSCILLATION 30 3.2 RELATIVIST]* DYNAMICS 30 3.3 NUCLEAR REACTORS 31 3.4
DISTRIBUTED NETWORKS (LONG LINE WITH TUNNEL DIODE) 32 3.5 HEAT FLOW IN
MATERIALS WITH MEMORY 34 3.6 MODELS OF LASERS 35 3.7 NEURAL NETWORK 35
4. MODELS WITH DELAYS IN TECHNICAL PROBLEMS 36 4.1 INFEED GRINDING AND
CUTTING 36 4.2 TECHNOLOGICAL DELAY 38 4.3 CAR CHASING 39 4.4 SHIP COURSE
STABILIZATION 39 4.5 PROCESS OF COMBUSTION IN SMALL ROCKETS 39 4.6
DELAY-DIFL ERENTIAL EQUATIONS IN ENGINEERING APPLICATIONS 40 5.
AFTEREFFECT IN BIOLOGY 61 5.1 EVOLUTION EQUATIONS OF A SINGLE SPECIES 61
VLLL 5.2 INTERACTION OF TWO SPECIES 65 5.3 POPULATION DYNAMICS MODEL OF
N INTERACTING SPECIES 66 5.4 COEXISTENCE OF COMPETITIVE MICRO-ORGANISMS
67 5.5 CONTROL PROBLEMS IN ECOLOGY 67 5.6 CONTROL PROBLEMS IN
MICROBIOLOGY (CHEMOSTAT MODELS) 68 5.7 NICHOLSON BLOWFLIES MODEL 70 5.8
HELICAL MOVEMENT OF TIPS OF GROWING PLANTS 70 5.9 GRAZING SYSTEM 70 6.
AFTEREFFECT IN MEDICINE 71 6.1 MATHEMATICAL MODELS OF THE SUGAR QUANTITY
IN BLOOD 71 6.2 MODEL OF ARTERIAL BLOOD PRESSURE REGULATION 72 6.3
CANCER CHEMOTHERAPY 74 6.4 MATHEMATICAL MODELS OF LEARNING 74 6.5
MATHEMATICAL MODELS IN IMMUNOLOGY AND EPIDEMIOLOGY 75 6.6 MODEL OF THE
HUMAN IMMUNODEFICIENCY VIRUS (HIV) EPIDEMIC 75 6.7 MODEL OF SURVIVAL OF
RED BLOOD CELLS 78 6.8 VISION PROCESS IN THE COMPOUND EYE 78 6.9 HUMAN
RESPIRATORY SYSTEM 78 6.10 REGULATION OF GLUCOSE-INSULIN SYSTEM 79 6.11
A DISEASE TRANSMISSION MODEL 79 7. AFTEREFFECT IN ECONOMY AND OTHER
SCIENCES 80 7.1 OPTIMAL SKILL WITH RETARDED CONTROLS 80 7.2 OPTIMAL
ADVERTISING POLICIES 81 7.3 COMMODITY PRICE FLUCTUATIONS 82 7.4 MODEL OF
THE FISHING PROCESS 82 7.5 RIVER POLLUTION CONTROL 83 7.6 CONTROL OF
FINANCIAL MANAGEMENT 83 PART II. THEORETICAL BACKGROUND OF FUNCTIONAL
DIFFERENTIAL EQUATIONS CHAPTER 3. GENERAL THEORY 87 1. INTRODUCTION.
METHOD OF STEPS 87 1.1 NOTATION 87 1.2 CAUCHY PROBLEM FOR FDES 88 1.3
STEPS METHOD FOR FDES OF RETARDED TYPE (RDES) 89 1.4 STEPS METHODS FOR
FDES OF NEUTRAL TYPE (NDES) 1.5 PROBLEM FOR A PROCESS WITH AFTEREFFECT
RENEWAL 2. CAUCHY PROBLEM FOR RDES 2.1 BASIC SOLVABILITY THEOREM 2.2
VARIANTS 2.3 SEMIGROUP RELATION 2.4 ABSOLUTELY CONTINUOUS SOLUTIONS 2.5
RDES WITH INFINITE DELAY 2.6 FEATURES OF THE CAUCHY PROBLEM FOR RDES 3.
CAUCHY PROBLEM FOR NDES 3.1 SMOOTH SOLUTIONS 3.2 NDES WITH A FUNCTIONAL
OF INTEGRAL TYPE 3.3 APPLICATION OF THE STEPS METHOD 3.4 TRANSITION TO
THE OPERATOR EQUATION 3.5 HALE S FORM OF NDES 4. DIFFERENTIAL INCLUSIONS
OF RETARDED TYPE (RDIS) 4.1 INTRODUCTION 4.2 MULTIMAPS 4.3 SOLVABILITY
OF THE CAUCHY PROBLEM FOR RDIS 4.4 GENERALIZED SOLUTIONS OF RDES AND
RDIS 5. GENERAL LINEAR FDES WITH AFTEREFFECT 5.1 CAUCHY PROBLEM FOR
LINEAR RDES 5.2 GENERALIZATION 5.3 INTEGRAL REPRESENTATION FOR THE
SOLUTION OF THE CAUCHY PROBLEM (VARIATION OF CONSTANTS FORMULA) 5.4
ADJOINT EQUATION. PERIODIC SOLUTIONS 5.5 LINEAR NDES 5.6 SIMPLEST
NONAUTONOMOUS RDES OF THE FIRST AND SECOND ORDERS 6. LINEAR AUTONOMOUS
FDES 6.1 EXPONENTIAL SOLUTIONS OF LINEAR AUTONOMOUS RDES 6.2 SOLUTION OF
THE CAUCHY PROBLEM 6.3 EXAMPLE OF A SHOWERING PERSON 6.4 LINEAR
AUTONOMOUS NDES 7. HOPF BIFURCATION OF FDES 7.1 INTRODUCTION 7.2
EXAMPLE 177 7.3 GENERAL CASE 182 7.4 VARIANTS 186 7.5 EXAMPLE OF AN RDE
WITH CONSTANT DELAY: INTRASPECILIC STRUGGLE FOR A COMMON FOOD 187 7.6
EXAMPLE OF AN RDE WITH AUTOREGULATIVE DELAY: COMBUSTION IN THE CHAMBER
OF A TURBOJET ENGINE 189 7.7 EXAMPLE NDE: AUTO-OSCILLATION IN A LONG
LINE WITH TUNNEL DIOD 191 8. STOCHASTIC RETARDED DIFFERENTIAL EQUATIONS
(SRDES) 191 8.1 INITIAL VALUE PROBLEM 192 8.2 EXISTENCE AND UNIQUENESS
OF SOLUTION 194 8.3 SOME CHARACTERISTICS OF SOLUTIONS OF LINEAR
EQUATIONS 195 PART III. STABILITY CHAPTER 4. STABILITY OF RETARDED
DIFFERENTIAL EQUATIONS 199 1. LIAPUNOV S DIRECT METHOD 199 1.1 STABILITY
DEFINITIONS 199 1.2 STABILITY THEOREMS FOR EQUATIONS WITH BOUNDED DELAY
204 1.3 STABILITY OF EQUATIONS WITH UNBOUNDED DELAY 211 1.4 STABILITY OF
LINEAR NONAUTONOMOUS RDES 216 1.5 STABILITY OF LINEAR PERIODIC RDES 217
1.6 APPLICATION OF COMPARISON THEOREMS 222 1.7 STABILITY IN THE FIRST
APPROXIMATION 223 1.8 CASE OF NON-POSITIVE DERIVATIVE 224 2. LINEAR
AUTONOMOUS RDES 226 2.1 LAPLACE TRANSFORMATION 226 2.2 STABILITY
CONDITIONS 228 3. STABILITY INVESTIGATION METHODS FOR LINEAR AUTONOMOUS
RDES 232 3.1 INTRODUCTION 232 3.2 MIKHAILOV CRITERIUM 232 3.3 SCALAR
***TH ORDER EQUATIONS 233 3.4 EQUATIONS WITH DISCRETE DELAYS 236 4.
RAZUMIKHIN S METHOD 247 4.1 INTRODUCTION 247 XI 4.2 GUIDING FUNCTIONS
FOR SYSTEMS WITHOUT DELAY 248 4.3 GUIDING FUNCTIONATE FOR RDES 249 4.4
DIRECT APPLICATION OF LIAPUNOV FUNCTIONS TO RDES 251 4.5 THE MAIN IDEA
OF B.S. RAZUMIKHIN 251 4.6 IMPOSSIBILITY OF THE FIRST BREAKDOWN 252
4.7 PRECIZE FORMULATION 253 4.8 CONNECTION BETWEEN RAZUMIKHIN S METHOD
AND LIAPUNOV FUNCTIONALS 254 4.9 ASYMPTOTIC STABILITY 254 4.10
REFINEMENT OF ESTIMATIONS 255 4.11 EXAMPLE 255 4.12 TRANSFORMATION OF
RDES 258 4.13 OTHER APPLICATIONS OF RAZUMIKHIN S METHOD 260 CHAPTER 5.
STABILITY OF RDES WITH AUTONOMOUS LINEAR PART 263 1. NOTATIONS 263 2.
INSTABILITY 266 3. ESTIMATES FOR THE GREEN FUNCTION 270 4. A BOUND FOR A
REGION OF ATTRACTION 274 CHAPTER 6. LIAPUNOV FUNCTIONALS FOR CONCRETE
FDES 279 1. STATEMENT OF THE PROBLEM 279 2. FORMAL DESCRIPTION OF THE
PROCEDURE 280 3. DISSIPATIVE SYSTEMS 284 3.1 STABILITY 284 3.2
EXPONENTIAL CONTRACTIVITY 291 4. STABILITY IN THE FIRST APPROXIMATION
293 4.1 EXPONENTIALLY STABLE LINEAR PART 294 4.2 SMOOTH COEFFICIENTS 294
5. SCALAR RDES 296 5.1 SCALAR EQUATIONS OF N-TH ORDER 296 5.2 SCALAR
EQUATIONS OF SECOND ORDER 299 5.3 STABILITY OF CHEMOSTAT 304 CHAPTER 7.
RICCATI TYPE STABILITY CONDITIONS OF SOME LINEAR SYSTEMS WITH DELAY 307
1. INTRODUCTION 307 2. SPECIAL CASE 309 XII 2.1 THE STABILITY CONDITION
FOR THIS CASE 309 2.2 AN APPLICATION OF A FORM OF NDE 310 2.3 ONE MORE
STABILITY CONDITION 312 3. DISCRETE DELAY-INDEPENDENT STABILITY
CONDITIONS 313 4. DELAY-DEPENDENT STABILITY CONDITIONS FOR EQUATIONS
WITH DISCRETE DELAYS 316 4.1 THE STABILITY CONDITION 317 4.2 AN
APPLICATION OF A FORM OF NDE 318 4.3 ONE MORE STABILITY CONDITION 319 5.
DISTRIBUTED DELAY 321 5.1 THE STABILITY CONDITION 322 5.2 AN APPLICATION
OF A FORM OF NDE 323 5.3 ONE MORE STABILITY CONDITION 324 CHAPTER 8.
STABILITY OF NEUTRAL TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS 329 1.
DIRECT LIAPUNOV S METHOD 329 1.1 DEGENERATE LIAPUNOV FUNCTIONALS 329 1.2
STABIBTY IN A FIRST APPROXIMATION 335 1.3 THE USE OF FUNCTIONALS
DEPENDING ON DERIVATIVES 336 1.4 INSTABILITY OF NDES 337 2. STABILITY OF
LINEAR NDES 343 2.1 LINEAR AUTONOMOUS NDES 343 2.2 SCALAR NDES 346 2.3
STABILITY OF NDES WITH DISCRETE DELAYS 349 2.4 THE INFLUENCE OF SMALL
DELAYS ON STABILITY 351 2.5 LINEAR INHOMOGENEOUS NDES 352 2.6
BOUNDEDNESS OF DERIVATIVES FOR LINEAR NDES 352 2.7 BOUNDEDNESS OF
DERIVATIVES FOR NONLINEAR NDES 353 2.8 LINEAR PERIODIC NDES 355 CHAPTER
9. APPLICATION OF THE DIRECT LIAPUNOV METHOD 359 1. DESCRIPTION OF THE
PROCEDURE 359 2. SCALAR NDES OF N-TH ORDER 362 3. LINEAR NDES 367 3.1
THE STABILITY CONDITION 367 3.2 ANOTHER STABILITY CONDITION 368 3.3 THE
SUMMARIZING RESULT 370 4. NONLINEAR NDES 371 5. STABILITY OF THE SECOND
ORDER NDES 375 6. AN ILLUSTRATIVE EXAMPLE FOR DIMENSION N = 3 380 7.
MATRIX RICCATI EQUATIONS IN STABILITY OF NDES 386 CHAPTER 10. STABILITY
OF STOCHASTIC, FUNCTIONAL DIFFERENTIAL EQUATIONS 387 1. STATEMENT OF THE
PROBLEM 387 1.1 DEFINITIONS OF STABILITY 387 1.2 ITOE S FORMULA 389 2.
LIAPUNOV S DIRECT METHOD 389 2.1 ASYMPTOTIC STABILITY 389 2.2 EXAMPLES
390 2.3 EXPONENTIAL STABILITY 394 2.4 STABILITY IN THE FIRST
APPROXIMATION 395 2.5 STABILITY UNDER PERSISTENT DISTURBANCES 396 3.
BOUNDEDNESS OF MOMENTS OF SOLUTIONS 397 3.1 GENERAL CONDITIONS FOR
BOUNDEDNESS OF MOMENTS 397 3.2 SCALAR SR DE 398 3.3 SECOND ORDER SRDE
401 4. CONSTRUCTION OF LIAPUNOV FUNCTIONALS FOR SNDES 402 4.1 STATEMENT
OF THE PROBLEM 402 4.2 DESCRIPTION OF THE PROCEDURE 404 4.3 SCALAR SN DE
405 4.4 NONLINEAR EXAMPLE 407 5. RICCATI MATRIX EQUATIONS IN STABILITY
OF LINEAR SRDES 415 PART IV. BOUNDARY VALUE PROBLEMS AND PERIODIC
SOLUTIONS OF DIFFERENTIAL EQUATIONS CHAPTER 11. BOUNDARY VALUE PROBLEMS
FOR FUNCTIONAL DIFFERENTIAL EQUATIONS 443 1. BOUNDARY VALUE PROBLEMS FOR
FDES OF EVOLUTIONARY TYPE 443 1.1 INTRODUCTION 443 1.2 PROBLEMS WITH A
FINITE DEFECT 443 1.3 HALANAY S BOUNDARY VALUE PROBLEM 446 1.4 PERIODIC
PROBLEM 448 2. BOUNDARY VALUE PROBLEMS FOR FDES OF NONEVOLUTIONARY TYPE
449 2.1 FDES WITH UNIQUE PRINCIPAL TERM 450 2.2 FDES WITH NONUNIQUE
PRINCIPAL TERM 453 CHAPTER 12. FREDHOLM ALTERNATIVE FOR PERIODIC
SOLUTIONS OF LINEAR FD ES 459 1. EXISTENCE OF PERIODIC SOLUTIONS 459 1.1
STATEMENT OF THE PROBLEM 459 1.2 CONDITIONS OF THE FREDHOLM ALTERNATIVE
VALIDITY 461 2. CONNECTION BETWEEN BOUNDEDNESS AND PERIODICITY 467 3.
PERIODIC SOLUTION OF LINEAR DIFFERENCE EQUATIONS (DCES) 468 3.1
STATEMENT OF THE PROBLEM 468 3.2 STATIONARY CASE. COMMENSURABLE SHIFTS
OF THE ARGUMENT 468 3.3 ARBITRARY DELAYS 470 3.4 VARIABLE COEFFICIENTS,
DELAYS DIVISIBLE BY A PERIOD 471 3.5 VARIABLE COEFFICIENTS, DELAYS
COMMENSURABLE WITH A PERIOD 474 3.6 VARIABLE COEFFICIENTS, ARBITRARY
CONSTANT DELAYS 478 4. NDES WITH SMALL NONLINEARITIES 479 5. PERIODIC
SOLUTIONS OF AUTONOMOUS FDES WITH SMALL PARAMETER 481 CHAPTER 13.
GENERALIZED PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS 489
1. SOME PREREQUISITES 489 2. CONDITIONS OF EXISTENCE OF PERIODIC
SOLUTIONS 491 3. RELATION BETWEEN STABILITY AND PERIODICITY 494 3.1
APPLICATION OF THE DIRECT LIAPUNOV METHOD 494 3.2 STABILITY OF PERIODIC
SOLUTIONS 498 4. PERIODIC SOLUTIONS OF CONCRETE CLASSES OF EQUATIONS 499
4.1 THE CASE OF QUASILINEAR DETERMINISTIC EQUATION 499 4.2 LINEAR
EQUATIONS 502 5. PERIODIC SOLUTIONS OF THE ITOE S SFDES 503 5.1 EXISTENCE
OF PERIODIC SOLUTIONS 503 5.2 SCALAR SRDES 506 5.3 METHOD OF LIAPUNOV
FUNCTIONALS 510 5.4 UNIQUENESS OF PERIODIC SOLUTIONS 517 XV PART V.
CONTROL AND ESTIMATION IN HEREDITARY SYSTEMS CHAPTER 14. PROBLEMS OF
CONTROL FOR DETERMINISTIC FDES 523 1. THE DYNAMIC PROGRAMMING METHOD FOR
DETERMINISTIC RDES. BELLMAN S EQUATION 523 1.1 STATEMENT OF THE PROBLEM
523 1.2 OPTIMALITY CONDITIONS 525 2. LINEAR QUADRATIC PROBLEMS 526 2.1
OPTIMAL CONTROL SYNTHESIS 526 2.2 EXACT SOLUTION 528 2.3 SYSTEMS WITH
DELAYS IN THE CONTROL 529 2.4 EFFECTS OF DELAYS IN REGULATORS 532 2.5
NDE 533 3. OPTIMAL CONTROL OF BILINEAR HEREDITARY SYSTEMS 534 3.1
OPTIMALITY CONDITIONS 534 3.2 CONSTRUCTION OF THE OPTIMAL CONTROL
SYNTHESIS 535 3.3 MODEL OF OPTIMAL FEEDBACK CONTROL FOR MICROBIAL GROWTH
538 4. CONTROL PROBLEMS WITH PHASE CONSTRAINT FORMULA 538 4.1 GENERAL
OPTIMALITY CONDITIONS 538 4.2 EQUATIONS WITH DISCRETE DELAYS 540 5.
NECESSARY OPTIMALITY CONDITIONS 543 5.1 SYSTEMS WITH STATE DELAYS 543
5.2 SYSTEMS WITH DELAYS IN THE CONTROL 545 5.3 SYSTEMS WITH DISTRIBUTED
DELAYS 546 5.4 LINEAR SYSTEMS WITH DISCRETE AND DISTRIBUTED DELAYS 547
5.5 NEUTRAL TYPE SYSTEMS 549 6. ADAPTIVE CONTROL OF FDES 550 6.1 SCALAR
EQUATIONS 550 6.2 DELAY IDENTIFICATION 553 6.3 MULTIDIMENSIONAL SYSTEMS
554 XVI CHAPTER 15. OPTIMAL CONTROL OF STOCHASTIC DELAY SYSTEMS 557 1.
DYNAMIC PROGRAMMING METHOD FOR CONTROLLED STOCHASTIC HEREDITARY
PROCESSES 557 2. THE LINEAR QUADRATIC PROBLEM 558 2.1 BELLMAN FUNCTIONAL
AND OPTIMAL CONTROL 558 2.2 APPROXIMATE SOLUTION 560 2.3 SOME
GENERALIZATIONS 564 3. APPROXIMATE OPTIMAL CONTROL FOR EQUATIONS WITH
SMALL PARAMETERS 564 3.1 FORMAL ALGORITHM 564 3.2 QUASILINEAR SYSTEMS
WITH QUADRATIC COST 566 4. ANOTHER APPROACH TO THE PROBLEM OF OPTIMAL
SYNTHESIS CONTROL 568 4.1 ADMISSIBLE FUNCTIONALS 568 4.2 QUASILINEAR
QUADRATIC PROBLEMS 569 CHAPTER 16. STATE ESTIMATES OF STOCHASTIC SYSTEMS
WITH DELAY 573 1. FILTERING OF GAUSSIAN PROCESSES 573 1.1 PROBLEM
STATEMENT 573 1.2 INTEGRAL REPRESENTATION FOR THE OPTIMAL ESTIMATE 574
1.3 THE FUNDAMENTAL FILTERING EQUATION 575 1.4 DUAL OPTIMAL CONTROL
PROBLEM 578 1.5 PARTICULAR CASES 580 1.6 DEPENDENCE OF THE ERROR OF THE
OPTIMAL ESTIMATE ON THE DELAY 581 1.7 SOME GENERALIZATIONS 587 2.
FILTERING OF SOLUTIONS OF ITO S EQUATIONS WITH DELAY 589 2.1 PROBLEM
STATEMENT 589 2.2 DUAL CONTROL PROBLEM 590 3. MINIMAX FILTERING IN
SYSTEMS WITH DELAY 592 3.1 STATEMENT OF THE PROBLEM 592 3.2 APPROXIMATE
SOLUTION 595 BIBLIOGRAPHY 601 INDEX 643
|
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| indexdate | 2024-07-09T18:29:43Z |
| institution | BVB |
| isbn | 0792355040 |
| language | English |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Kolmanovskij, Vladimir B. Verfasser aut Introduction to the theory and applications of functional differential equations by V. Kolmanovskii and A. Myshkis Dordrecht [u.a.] Kluwer 1999 XVI, 648 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 463 Funktional-Differentialgleichung (DE-588)4155668-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktional-Differentialgleichung (DE-588)4155668-9 s DE-604 Myškis, Anatolij D. 1920-2009 Verfasser (DE-588)106775057 aut Mathematics and its applications 463 (DE-604)BV008163334 463 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008530323&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolmanovskij, Vladimir B. Myškis, Anatolij D. 1920-2009 Introduction to the theory and applications of functional differential equations Mathematics and its applications Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| subject_GND | (DE-588)4155668-9 (DE-588)4151278-9 |
| title | Introduction to the theory and applications of functional differential equations |
| title_auth | Introduction to the theory and applications of functional differential equations |
| title_exact_search | Introduction to the theory and applications of functional differential equations |
| title_full | Introduction to the theory and applications of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_fullStr | Introduction to the theory and applications of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_full_unstemmed | Introduction to the theory and applications of functional differential equations by V. Kolmanovskii and A. Myshkis |
| title_short | Introduction to the theory and applications of functional differential equations |
| title_sort | introduction to the theory and applications of functional differential equations |
| topic | Funktional-Differentialgleichung (DE-588)4155668-9 gnd |
| topic_facet | Funktional-Differentialgleichung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008530323&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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