Oscillation theory of delay differential equations: with applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1991
|
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 344 - 364 |
| Physical Description: | XII, 368 S. |
| ISBN: | 0198535821 |
Staff View
MARC
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| 100 | 1 | |a Györi, I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Oscillation theory of delay differential equations |b with applications |c I. Györi and G. Ladas |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1991 | |
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Record in the Search Index
| _version_ | 1804118808815730688 |
|---|---|
| adam_text | CONTENTS
1 PRELIMINARIES 1
1.1 Some basic existenc and uniqueness theorems 1
1.2 Exponential boundedness of solutions 10
1.3 The Laplace transform 13
1.4 The z transform 15
1.5 Some basic lemmas 17
1.6 Some basic lemmas on differential inequalities 23
1.7 Some useful theorems from analysis 27
1.8 Notes 31
2 OSCILLATIONS OF LINEAR SCALAR
DELAY EQUATIONS 32
2.1 Necessary and sufficient conditions for oscillations.
The autonomous case 33
2.2 Explicit conditions for oscillations 37
2.3 Sufficient conditions for oscillations and for non oscillations.
The non autonomous case 42
2.4 Oscillations of delay differential equations with asymp¬
totically constant coefficients 46
2.5 Nicholson s blowflies 51
2.6 Oscillations in non autonomous equations with positive
and negative coefficients 54
2.7 Notes 55
2.8 Open problems 56
3 GENERALIZED CHARACTERISTIC EQUATION
AND EXISTENCE OF POSITIVE SOLUTIONS 58
3.1 A generalized characteristic equation 58
3.2 Differential inequalities and comparison results for positive
solutions 64
3.3 Existence of positive solutions 70
3.4 Sufficient conditions for the oscillation of non autonomous
equations 74
3.5 Notes 79
3.6 Open problems 80
X CONTENTS
4 LINEARIZED OSCILLATION THEORY AND
APPLICATIONS TO MATHEMATICAL BIOLOGY 81
4.1 Linearized oscillation theory 82
4.2 Time lags in a food limited population model 84
4.3 Oscillations in the delay logistic equation with several delays 87
4.4 The Lasota Wazewska model for the survival of red blood
cells 89
4.5 Notes 90
4.6 Open problems 90
5 OSCILLATIONS OF SYSTEMS OF DELAY
EQUATIONS 91
5.1 Necessary and sufficient conditions for the oscillation of
linear autonomous systems 92
5.2 Explicit conditions for oscillations and non oscillations of
linear autonomous systems 95
5.3 Sufficient conditions for the oscillation of linear non autono¬
mous systems 100
5.4 Oscillations of a system of delay logistic equations 102
5.5 Notes 110
5.6 Open problems 110
6 OSCILLATIONS OF NEUTRAL DIFFERENTIAL
EQUATIONS 111
6.1 Oscillations and asymptotic behaviour of scalar neutral
delay differential equations 112
6.2 Oscillations of scalar neutral equations with mixed argu¬
ments 115
6.3 Necessary and sufficient conditions for the oscillation of
systems of neutral equations 123
6.4 Oscillations of scalar neutral equations with variable coef¬
ficients 125
6.5 Differential inequalities and comparison theorems 130
6.6 Linearized oscillations for neutral equations 135
6.7 Existence of positive solutions 140
6.8 Oscillations in neutral delay logistic differential equations 148
6.9 Oscillations in non autonomous equations with several
delays 151
6.10 Oscillations in a system of neutral equations 156
6.11 Notes 159
6.12 Open problems 160
CONTENTS xi
7 OSCILLATIONS OF DELAY DIFFERENCE
EQUATIONS 162
7.1 Necessary and sufficient conditions for the oscillation of
linear systems of difference equations 163
7.2 Explicit necessary and sufficient conditions for oscillations 166
7.3 Sufficient conditions for oscillations 169
7.4 Linearized oscillations for delay difference equations 172
7.5 A sharp condition for the oscillation of difference equations 178
7.6 Difference inequalities 184
7.7 Equations with positive and negative coefficients 187
7.8 Existence of positive solutions 190
7.9 Oscillations in a discrete delay logistic model 194
7.10 Notes 196
7.11 Open problems 196
8 OSCILLATIONS OF EQUATIONS WITH
PIECEWISE CONSTANT ARGUMENTS 198
8.1 Necessary and sufficient conditions for the oscillation of
linear systems with piecewise constant arguments 199
8.2 Linearized oscillations and the logistic equation with piece
wise constant arguments 205
8.3 Oscillations in non autonomous equations with piecewise
constant arguments 209
8.4 Oscillations in equations of alternately retarded and ad¬
vanced type 214
8.5 Oscillations in equations with continuous and piecewise
constant arguments 217
8.6 Notes 222
8.7 Open problems 223
9 OSCILLATIONS OF INTEGRODIFFERENTIAL
EQUATIONS 225
9.1 Oscillations of linear integrodifferential equations 226
9.2 Comparison results for integrodifferential equations of
Volterra type 231
9.3 Positive solutions of integrodifferential equations with un¬
bounded delay 235
9.4 Oscillation in Volterra s integrodifferential equation 240
9.5 Notes 247
9.6 Open problems 247
Xii CONTENTS
10 OSCILLATIONS OF SECOND AND HIGHER
ORDER EQUATIONS 248
10.1 Linearized oscillations for second order differential equa¬
tionsâ€â€
|
| any_adam_object | 1 |
| author | Györi, I. Ladas, Gerasimos E. |
| author_facet | Györi, I. Ladas, Gerasimos E. |
| author_role | aut aut |
| author_sort | Györi, I. |
| author_variant | i g ig g e l ge gel |
| building | Verbundindex |
| bvnumber | BV004693259 |
| classification_rvk | SK 520 |
| classification_tum | MAT 340f |
| ctrlnum | (OCoLC)246828897 (DE-599)BVBBV004693259 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004693259 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:16:11Z |
| institution | BVB |
| isbn | 0198535821 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002881399 |
| oclc_num | 246828897 |
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| owner_facet | DE-91 DE-BY-TUM DE-12 DE-384 DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| physical | XII, 368 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Györi, I. Verfasser aut Oscillation theory of delay differential equations with applications I. Györi and G. Ladas Oxford Clarendon Press 1991 XII, 368 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Literaturverz. S. 344 - 364 Schwingung (DE-588)4053999-4 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Schwingung (DE-588)4053999-4 s DE-604 Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s Ladas, Gerasimos E. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002881399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Györi, I. Ladas, Gerasimos E. Oscillation theory of delay differential equations with applications Schwingung (DE-588)4053999-4 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4053999-4 (DE-588)4199298-2 (DE-588)4020929-5 |
| title | Oscillation theory of delay differential equations with applications |
| title_auth | Oscillation theory of delay differential equations with applications |
| title_exact_search | Oscillation theory of delay differential equations with applications |
| title_full | Oscillation theory of delay differential equations with applications I. Györi and G. Ladas |
| title_fullStr | Oscillation theory of delay differential equations with applications I. Györi and G. Ladas |
| title_full_unstemmed | Oscillation theory of delay differential equations with applications I. Györi and G. Ladas |
| title_short | Oscillation theory of delay differential equations |
| title_sort | oscillation theory of delay differential equations with applications |
| title_sub | with applications |
| topic | Schwingung (DE-588)4053999-4 gnd Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Schwingung Differentialgleichung mit nacheilendem Argument Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002881399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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