Existence Theory for Nonlinear Ordinary Differential Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
398 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424253 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1997 xx o|||| 00||| eng d | ||
| 020 | |a 9789401715171 |c Online |9 978-94-017-1517-1 | ||
| 020 | |a 9789048148356 |c Print |9 978-90-481-4835-6 | ||
| 024 | 7 | |a 10.1007/978-94-017-1517-1 |2 doi | |
| 035 | |a (OCoLC)1184493444 | ||
| 035 | |a (DE-599)BVBBV042424253 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.352 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a O’Regan, Donal |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Existence Theory for Nonlinear Ordinary Differential Equations |c by Donal O’Regan |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1997 | |
| 300 | |a 1 Online-Ressource (VII, 200 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematics and Its Applications |v 398 | |
| 500 | |a We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Integral equations | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Differential Equations | |
| 650 | 4 | |a Ordinary Differential Equations | |
| 650 | 4 | |a Integral Equations | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Anfangswertproblem |0 (DE-588)4001991-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Existenzaussage |0 (DE-588)4153313-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Existenzsatz |0 (DE-588)4297175-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |D s |
| 689 | 0 | 1 | |a Anfangswertproblem |0 (DE-588)4001991-3 |D s |
| 689 | 0 | 2 | |a Existenzsatz |0 (DE-588)4297175-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |D s |
| 689 | 1 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 1 | 2 | |a Existenzsatz |0 (DE-588)4297175-5 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 689 | 2 | 0 | |a Nichtlineare gewöhnliche Differentialgleichung |0 (DE-588)4478411-9 |D s |
| 689 | 2 | 1 | |a Existenzaussage |0 (DE-588)4153313-6 |D s |
| 689 | 2 | |8 3\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-017-1517-1 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027859670 | |
Datensatz im Suchindex
| _version_ | 1819294259828752384 |
|---|---|
| any_adam_object | |
| author | O’Regan, Donal |
| author_facet | O’Regan, Donal |
| author_role | aut |
| author_sort | O’Regan, Donal |
| author_variant | d o do |
| building | Verbundindex |
| bvnumber | BV042424253 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184493444 (DE-599)BVBBV042424253 |
| dewey-full | 515.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.352 |
| dewey-search | 515.352 |
| dewey-sort | 3515.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-1517-1 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03987nam a2200697zcb4500</leader><controlfield tag="001">BV042424253</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1997 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401715171</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-017-1517-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048148356</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-4835-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-017-1517-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184493444</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424253</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.352</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">O’Regan, Donal</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Existence Theory for Nonlinear Ordinary Differential Equations</subfield><subfield code="c">by Donal O’Regan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VII, 200 p)</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">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematics and Its Applications</subfield><subfield code="v">398</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ordinary Differential Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral Equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Anfangswertproblem</subfield><subfield code="0">(DE-588)4001991-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Existenzaussage</subfield><subfield code="0">(DE-588)4153313-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Existenzsatz</subfield><subfield code="0">(DE-588)4297175-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Anfangswertproblem</subfield><subfield code="0">(DE-588)4001991-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Existenzsatz</subfield><subfield code="0">(DE-588)4297175-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Randwertproblem</subfield><subfield code="0">(DE-588)4048395-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Existenzsatz</subfield><subfield code="0">(DE-588)4297175-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Nichtlineare gewöhnliche Differentialgleichung</subfield><subfield code="0">(DE-588)4478411-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Existenzaussage</subfield><subfield code="0">(DE-588)4153313-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-017-1517-1</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859670</subfield></datafield></record></collection> |
| id | DE-604.BV042424253 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:29Z |
| institution | BVB |
| isbn | 9789401715171 9789048148356 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859670 |
| oclc_num | 1184493444 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VII, 200 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematics and Its Applications |
| spelling | O’Regan, Donal Verfasser aut Existence Theory for Nonlinear Ordinary Differential Equations by Donal O’Regan Dordrecht Springer Netherlands 1997 1 Online-Ressource (VII, 200 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 398 We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here Mathematics Integral equations Operator theory Differential Equations Ordinary Differential Equations Integral Equations Operator Theory Mathematik Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf Existenzaussage (DE-588)4153313-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd rswk-swf Existenzsatz (DE-588)4297175-5 gnd rswk-swf Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 s Anfangswertproblem (DE-588)4001991-3 s Existenzsatz (DE-588)4297175-5 s 1\p DE-604 Randwertproblem (DE-588)4048395-2 s 2\p DE-604 Existenzaussage (DE-588)4153313-6 s 3\p DE-604 https://doi.org/10.1007/978-94-017-1517-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | O’Regan, Donal Existence Theory for Nonlinear Ordinary Differential Equations Mathematics Integral equations Operator theory Differential Equations Ordinary Differential Equations Integral Equations Operator Theory Mathematik Anfangswertproblem (DE-588)4001991-3 gnd Existenzaussage (DE-588)4153313-6 gnd Randwertproblem (DE-588)4048395-2 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd Existenzsatz (DE-588)4297175-5 gnd |
| subject_GND | (DE-588)4001991-3 (DE-588)4153313-6 (DE-588)4048395-2 (DE-588)4478411-9 (DE-588)4297175-5 |
| title | Existence Theory for Nonlinear Ordinary Differential Equations |
| title_auth | Existence Theory for Nonlinear Ordinary Differential Equations |
| title_exact_search | Existence Theory for Nonlinear Ordinary Differential Equations |
| title_full | Existence Theory for Nonlinear Ordinary Differential Equations by Donal O’Regan |
| title_fullStr | Existence Theory for Nonlinear Ordinary Differential Equations by Donal O’Regan |
| title_full_unstemmed | Existence Theory for Nonlinear Ordinary Differential Equations by Donal O’Regan |
| title_short | Existence Theory for Nonlinear Ordinary Differential Equations |
| title_sort | existence theory for nonlinear ordinary differential equations |
| topic | Mathematics Integral equations Operator theory Differential Equations Ordinary Differential Equations Integral Equations Operator Theory Mathematik Anfangswertproblem (DE-588)4001991-3 gnd Existenzaussage (DE-588)4153313-6 gnd Randwertproblem (DE-588)4048395-2 gnd Nichtlineare gewöhnliche Differentialgleichung (DE-588)4478411-9 gnd Existenzsatz (DE-588)4297175-5 gnd |
| topic_facet | Mathematics Integral equations Operator theory Differential Equations Ordinary Differential Equations Integral Equations Operator Theory Mathematik Anfangswertproblem Existenzaussage Randwertproblem Nichtlineare gewöhnliche Differentialgleichung Existenzsatz |
| url | https://doi.org/10.1007/978-94-017-1517-1 |
| work_keys_str_mv | AT oregandonal existencetheoryfornonlinearordinarydifferentialequations |