Theory of fuzzy differential equations and inclusions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Taylor & Francis
2003
|
| Series: | Series in mathematical analysis and applications
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 178 S. |
| ISBN: | 0415300738 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV023836609 | ||
| 003 | DE-604 | ||
| 005 | 20130507 | ||
| 007 | t| | ||
| 008 | 030925s2003 xx |||| 00||| eng d | ||
| 020 | |a 0415300738 |9 0-415-30073-8 | ||
| 035 | |a (OCoLC)249238902 | ||
| 035 | |a (DE-599)BVBBV023836609 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 |a DE-11 |a DE-703 | ||
| 082 | 0 | |a 515.35 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a SK 920 |0 (DE-625)143272: |2 rvk | ||
| 100 | 1 | |a Lakshmikantham, Vangipuram |d 1926-2012 |e Verfasser |0 (DE-588)104268050 |4 aut | |
| 245 | 1 | 0 | |a Theory of fuzzy differential equations and inclusions |c V. Lakshmikantham and R. N. Mohapatra |
| 264 | 1 | |a London [u.a.] |b Taylor & Francis |c 2003 | |
| 300 | |a IX, 178 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series in mathematical analysis and applications |v 6 | |
| 650 | 0 | 7 | |a Differentialinklusion |0 (DE-588)4149777-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fuzzy-Menge |0 (DE-588)4061868-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fuzzy-Menge |0 (DE-588)4061868-7 |D s |
| 689 | 0 | 1 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
| 689 | 0 | 2 | |a Differentialinklusion |0 (DE-588)4149777-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Mohapatra, Ram N. |e Verfasser |4 aut | |
| 830 | 0 | |a Series in mathematical analysis and applications |v 6 |w (DE-604)BV013405523 |9 6 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478730&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017478730 | |
Record in the Search Index
| _version_ | 1826831283589742592 |
|---|---|
| adam_text |
THEORY OF FUZZY DIFFERENTIAL EQUATIONS AND INCLUSIONS V. LAKSHMIKANTHAM
AND R. N. MOHAPATRA TAYLOR & FRANCIS TAYLOR & FRANCIS CROUP LONDON AND
NEW YORK CONTENTS PREFACE VII 1 FUZZY SETS 1 1.1 INTRODUCTION 1 1.2
FUZZY SETS 2 1.3 THE HAUSDORFF METRIC 5 1.4 SUPPORT FUNCTIONS 8 1.5 THE
SPACE E N 10 1.6 THE METRIC SPACE (", *) 17 1.7 NOTES AND COMMENTS 21 2
CALCULUS OF FUZZY FUNCTIONS 23 2.1 INTRODUCTION 23 2.2 CONVERGENCE OF
FUZZY SETS 23 2.3 MEASURABILITY 35 2.4 INTEGRABILITY 37 2.5
DIFFERENTIABILITY 42 2.6 NOTES AND COMMENTS 47 3 FUNDAMENTAL THEORY 49
3.1 INTRODUCTION 49 3.2 INITIAL VALUE PROBLEM 50 3.3 EXISTENCE 52 3.4
COMPARISON THEOREMS 53 3.5 CONVERGENCE OF SUCCESSIVE APPROXIMATIONS 58
3.6 CONTINUOUS DEPENDENCE 61 3.7 GLOBAL EXISTENCE 63 3.8 APPROXIMATE
SOLUTIONS 64 3.9 STABILITY CRITERIA 65 VI CONTENTS 3.10 NOTES AND
COMMENTS 69 4 LYAPUNOV-LIKE FUNCTIONS 71 4.1 INTRODUCTION 71 4.2
LYAPUNOV-LIKE FUNCTIONS 72 4.3 STABILITY CRITERIA 74 4.4 NONUNIFORM
STABILITY CRITERIA 77 4.5 CRITERIA FOR BOUNDEDNESS 82 4.6 FUZZY
DIFFERENTIAL SYSTEMS 87 4.7 THE METHOD OF VECTOR LYAPUNOV FUNCTIONS 91
4.8 LINEAR VARIATION OF PARAMETERS FORMULA 94 4.9 NOTES AND COMMENTS 97
5 MISCELLANEOUS TOPICS 99 5.1 INTRODUCTION 99 5.2 FUZZY DIFFERENCE
EQUATIONS 100 5.3 IMPULSIVE FUZZY DIFFERENTIAL EQUATIONS 104 5.4 FUZZY
DIFFERENTIAL EQUATIONS WITH DELAY 110 5.5 HYBRID FUZZY DIFFERENTIAL
EQUATIONS 114 5.6 FIXED POINTS OF FUZZY MAPPINGS 117 5.7 BOUNDARY VALUE
PROBLEM 120 5.8 FUZZY EQUATIONS OF VOLTERRA TYPE 123 5.9 A NEW CONCEPT
OF STABILITY 126 5.10 NOTES AND COMMENTS 132 6 FUZZY DIFFERENTIAL
INCLUSIONS 133 6.1 INTRODUCTION 133 6.2 FORMULATION OF FUZZY
DIFFERENTIAL INCLUSIONS 136 6.3 DIFFERENTIAL INCLUSIONS 140 6.4 FUZZY
DIFFERENTIAL INCLUSIONS 144 6.5 THE VARIATION OF CONSTANTS FORMULA 150
6.6 FUZZY VOLTERRA INTEGRAL EQUATIONS 155 6.7 NOTES AND COMMENTS 166
BIBLIOGRAPHY 167 INDEX 177 |
| any_adam_object | 1 |
| author | Lakshmikantham, Vangipuram 1926-2012 Mohapatra, Ram N. |
| author_GND | (DE-588)104268050 |
| author_facet | Lakshmikantham, Vangipuram 1926-2012 Mohapatra, Ram N. |
| author_role | aut aut |
| author_sort | Lakshmikantham, Vangipuram 1926-2012 |
| author_variant | v l vl r n m rn rnm |
| building | Verbundindex |
| bvnumber | BV023836609 |
| classification_rvk | SK 520 SK 920 |
| ctrlnum | (OCoLC)249238902 (DE-599)BVBBV023836609 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zcb4500</leader><controlfield tag="001">BV023836609</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130507</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">030925s2003 xx |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0415300738</subfield><subfield code="9">0-415-30073-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249238902</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023836609</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.35</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 920</subfield><subfield code="0">(DE-625)143272:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lakshmikantham, Vangipuram</subfield><subfield code="d">1926-2012</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)104268050</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Theory of fuzzy differential equations and inclusions</subfield><subfield code="c">V. Lakshmikantham and R. N. Mohapatra</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London [u.a.]</subfield><subfield code="b">Taylor & Francis</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 178 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Series in mathematical analysis and applications</subfield><subfield code="v">6</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialinklusion</subfield><subfield code="0">(DE-588)4149777-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fuzzy-Menge</subfield><subfield code="0">(DE-588)4061868-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fuzzy-Menge</subfield><subfield code="0">(DE-588)4061868-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Differentialgleichung</subfield><subfield code="0">(DE-588)4012249-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Differentialinklusion</subfield><subfield code="0">(DE-588)4149777-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mohapatra, Ram N.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Series in mathematical analysis and applications</subfield><subfield code="v">6</subfield><subfield code="w">(DE-604)BV013405523</subfield><subfield code="9">6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478730&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017478730</subfield></datafield></record></collection> |
| id | DE-604.BV023836609 |
| illustrated | Not Illustrated |
| indexdate | 2025-03-17T09:01:15Z |
| institution | BVB |
| isbn | 0415300738 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017478730 |
| oclc_num | 249238902 |
| open_access_boolean | |
| owner | DE-634 DE-11 DE-703 |
| owner_facet | DE-634 DE-11 DE-703 |
| physical | IX, 178 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Taylor & Francis |
| record_format | marc |
| series | Series in mathematical analysis and applications |
| series2 | Series in mathematical analysis and applications |
| spelling | Lakshmikantham, Vangipuram 1926-2012 Verfasser (DE-588)104268050 aut Theory of fuzzy differential equations and inclusions V. Lakshmikantham and R. N. Mohapatra London [u.a.] Taylor & Francis 2003 IX, 178 S. txt rdacontent n rdamedia nc rdacarrier Series in mathematical analysis and applications 6 Differentialinklusion (DE-588)4149777-6 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s Differentialgleichung (DE-588)4012249-9 s Differentialinklusion (DE-588)4149777-6 s DE-604 Mohapatra, Ram N. Verfasser aut Series in mathematical analysis and applications 6 (DE-604)BV013405523 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478730&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lakshmikantham, Vangipuram 1926-2012 Mohapatra, Ram N. Theory of fuzzy differential equations and inclusions Series in mathematical analysis and applications Differentialinklusion (DE-588)4149777-6 gnd Differentialgleichung (DE-588)4012249-9 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| subject_GND | (DE-588)4149777-6 (DE-588)4012249-9 (DE-588)4061868-7 |
| title | Theory of fuzzy differential equations and inclusions |
| title_auth | Theory of fuzzy differential equations and inclusions |
| title_exact_search | Theory of fuzzy differential equations and inclusions |
| title_full | Theory of fuzzy differential equations and inclusions V. Lakshmikantham and R. N. Mohapatra |
| title_fullStr | Theory of fuzzy differential equations and inclusions V. Lakshmikantham and R. N. Mohapatra |
| title_full_unstemmed | Theory of fuzzy differential equations and inclusions V. Lakshmikantham and R. N. Mohapatra |
| title_short | Theory of fuzzy differential equations and inclusions |
| title_sort | theory of fuzzy differential equations and inclusions |
| topic | Differentialinklusion (DE-588)4149777-6 gnd Differentialgleichung (DE-588)4012249-9 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Differentialinklusion Differentialgleichung Fuzzy-Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478730&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013405523 |
| work_keys_str_mv | AT lakshmikanthamvangipuram theoryoffuzzydifferentialequationsandinclusions AT mohapatraramn theoryoffuzzydifferentialequationsandinclusions |