Variational principles in mathematical physics, geometry, and economics: qualitative analysis of nonlinear equations and unilateral problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
136 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 368 S. |
| ISBN: | 9780521117821 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV036643244 | ||
| 003 | DE-604 | ||
| 005 | 20170921 | ||
| 007 | t | ||
| 008 | 100830s2010 |||| 00||| eng d | ||
| 020 | |a 9780521117821 |9 978-0-521-11782-1 | ||
| 035 | |a (OCoLC)699535582 | ||
| 035 | |a (DE-599)BVBBV036643244 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 | ||
| 100 | 1 | |a Kristály, Alexandru |e Verfasser |0 (DE-588)142317306 |4 aut | |
| 245 | 1 | 0 | |a Variational principles in mathematical physics, geometry, and economics |b qualitative analysis of nonlinear equations and unilateral problems |c Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga |
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XV, 368 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 136 | |
| 650 | 0 | 7 | |a Anwendung |0 (DE-588)4196864-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Variationsprinzip |0 (DE-588)4062354-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Variationsprinzip |0 (DE-588)4062354-3 |D s |
| 689 | 0 | 1 | |a Anwendung |0 (DE-588)4196864-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rădulescu, Vicenţiu D. |d 1958- |e Sonstige |0 (DE-588)138708924 |4 oth | |
| 700 | 1 | |a Varga, Csaba György |e Sonstige |0 (DE-588)142227625 |4 oth | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications |v 136 |w (DE-604)BV000903719 |9 136 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020562916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020562916 | ||
Datensatz im Suchindex
| _version_ | 1804143256517214208 |
|---|---|
| adam_text | Contents
Foreword page
x
Preface
xii
Part I Variational principles in mathematical physics
1
1
Variational principles
3
1.1
Minimization techniques and Ekeland s variational principle
3
1.2
Borwein-Preiss variational principle
8
1.3
Minimax principles
12
1.4
Ricceri s variational results
19
1.5
H1 versus
С
local minimizers
28
1.6
Szulkin-type functionals
33
1.7
Pohozaev s fibering method
38
1.8
Historical comments
39
2
Variational inequalities
42
2.1
Introduction
42
2.2
Variational inequalities on unbounded strips
43
2.3
Area-type variational inequalities
55
2.4
Historical notes and comments
78
3
Nonlinear eigenvalue problems
81
3.1
Weighted Sobolev spaces
82
3.2
Eigenvalue problems
85
3.3 Superlinear
case
94
3.4
Sublinearcase
104
3.5
Comments and further perspectives
115
4
Elliptic systems of gradient type
117
4.1
Introduction
117
4.2
Formulation of the problems
117
4.3
Systems with
superlinear
potential
119
4.4
Systems with
sublinear
potential
127
4.5
Shift solutions for gradient systems
134
4.6
Historical notes and comments
144
viii Contents
5
Systems
with arbitrary growth nonlinearities
146
5.1
Introduction
146
5.2
Elliptic systems with mountain pass geometry
148
5.3
Elliptic systems with oscillatory terms
153
5.4
Comments and perspectives
160
6
Scalar field systems
162
6.1
Introduction
162
6.2
Multiple solutions of a double eigenvalue problem
163
6.3
Scalar field systems with nonlinear oscillatory terms
172
6.4
Applications
178
6.5
Historical notes and comments
182
7
Competition phenomena in Dirichlet problems
183
7.1
Introduction
184
7.2
Effects of the competition
185
7.3
A general location property
190
7.4
Nonlinearities with oscillation near the origin
192
7.5
Nonlinearities with oscillation at infinity
198
7.6
Perturbation from symmetry
205
7.7
Historical notes and comments
208
8
Problems to Part I
210
Part II Variational principles in geometry
215
9
Sublinear
problems on Riemannian manifolds
217
9.1
Introduction
217
9.2
Existence of two solutions
218
9.3
Existence of many global minima
224
9.4
Historical notes and comments
227
10
Asymptotically critical problems on spheres
228
10.1
Introduction
228
10.2
Group-theoretical argument
229
10.3
Arbitrarily small solutions
235
10.4
Arbitrarily large solutions
242
10.5
Historical notes, comments, and perspectives
246
11
Equations with critical exponent
248
11.1
Introduction
248
11.2
Subcritical case
250
11.3
Critical case
252
11.4
Historical notes and comments
259
12
Problems to Part
11 261
Contents ix
Part
III Variational
principles in economics
265
13
Mathematical preliminaries
267
13.1
Metrics, geodesies, and flag curvature
267
13.2
Busemann-type inequalities on Finsler manifolds
271
13.3
Variational inequalities
277
14
Minimization of cost-functions on manifolds
278
14.1
Introduction
278
14.2
A necessary condition
280
14.3
Existence and uniqueness results
282
14.4
Examples on the
Finslerian-Poincaré
disc
285
14.5
Comments and further perspectives
287
15
Best approximation problems on manifolds
289
15.1
Introduction
289
15.2
Existence of projections
290
15.3
Geometric properties of projections
291
15.4
Geodesic convexity and Chebyshev sets
294
15.5
Optimal connection of two submanifolds
297
15.6
Remarks and perspectives
303
16
A variational approach to Nash equilibria
304
16.1
Introduction
304
16.2
Nash equilibria and variational inequalities
305
308
313
319
320
322
322
326
328
328
329
330
334
337
339
339
341
346
349
361
363
16.3
Nash equilibria for set-valued maps
16.4
Lack of convexity: a Riemannian approach
16.5
Historical comments and perspectives
17
Problems to Part III
Appendix A
Elements of convex analysis
A.I
Convex sets and convex functions
A.2
Convex analysis in Banach spaces
Appendix
В
Function spaces
B.I
Lebesgue spaces
B.2
Sobolev spaces
B.3
Compact embedding results
B.4
Sobolev spaces on Riemann manifolds
Appendix
С
Category and genus
Appendix
D
Clarke and Degiovanni gradients
D.I
Locally Lipschitz fimctionals
D.2
Continuous or lower semi-continuous fimctionals
Appendix
E
Elements of set-valued analysis
References
Notation index
Subject index
|
| any_adam_object | 1 |
| author | Kristály, Alexandru |
| author_GND | (DE-588)142317306 (DE-588)138708924 (DE-588)142227625 |
| author_facet | Kristály, Alexandru |
| author_role | aut |
| author_sort | Kristály, Alexandru |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV036643244 |
| ctrlnum | (OCoLC)699535582 (DE-599)BVBBV036643244 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01720nam a2200373 cb4500</leader><controlfield tag="001">BV036643244</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20170921 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100830s2010 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521117821</subfield><subfield code="9">978-0-521-11782-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)699535582</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036643244</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kristály, Alexandru</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)142317306</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Variational principles in mathematical physics, geometry, and economics</subfield><subfield code="b">qualitative analysis of nonlinear equations and unilateral problems</subfield><subfield code="c">Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 368 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">Encyclopedia of mathematics and its applications</subfield><subfield code="v">136</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Anwendung</subfield><subfield code="0">(DE-588)4196864-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Variationsprinzip</subfield><subfield code="0">(DE-588)4062354-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Variationsprinzip</subfield><subfield code="0">(DE-588)4062354-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Anwendung</subfield><subfield code="0">(DE-588)4196864-5</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">Rădulescu, Vicenţiu D.</subfield><subfield code="d">1958-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)138708924</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Varga, Csaba György</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)142227625</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Encyclopedia of mathematics and its applications</subfield><subfield code="v">136</subfield><subfield code="w">(DE-604)BV000903719</subfield><subfield code="9">136</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</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=020562916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020562916</subfield></datafield></record></collection> |
| id | DE-604.BV036643244 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:44:46Z |
| institution | BVB |
| isbn | 9780521117821 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020562916 |
| oclc_num | 699535582 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XV, 368 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Kristály, Alexandru Verfasser (DE-588)142317306 aut Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga Cambridge [u.a.] Cambridge Univ. Press 2010 XV, 368 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 136 Anwendung (DE-588)4196864-5 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 s Anwendung (DE-588)4196864-5 s DE-604 Rădulescu, Vicenţiu D. 1958- Sonstige (DE-588)138708924 oth Varga, Csaba György Sonstige (DE-588)142227625 oth Encyclopedia of mathematics and its applications 136 (DE-604)BV000903719 136 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020562916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kristály, Alexandru Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Encyclopedia of mathematics and its applications Anwendung (DE-588)4196864-5 gnd Variationsprinzip (DE-588)4062354-3 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4062354-3 |
| title | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_auth | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_exact_search | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_full | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga |
| title_fullStr | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga |
| title_full_unstemmed | Variational principles in mathematical physics, geometry, and economics qualitative analysis of nonlinear equations and unilateral problems Alexandru Kristály, Vicenţiu Rădulescu, Csaba György Varga |
| title_short | Variational principles in mathematical physics, geometry, and economics |
| title_sort | variational principles in mathematical physics geometry and economics qualitative analysis of nonlinear equations and unilateral problems |
| title_sub | qualitative analysis of nonlinear equations and unilateral problems |
| topic | Anwendung (DE-588)4196864-5 gnd Variationsprinzip (DE-588)4062354-3 gnd |
| topic_facet | Anwendung Variationsprinzip |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020562916&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT kristalyalexandru variationalprinciplesinmathematicalphysicsgeometryandeconomicsqualitativeanalysisofnonlinearequationsandunilateralproblems AT radulescuvicentiud variationalprinciplesinmathematicalphysicsgeometryandeconomicsqualitativeanalysisofnonlinearequationsandunilateralproblems AT vargacsabagyorgy variationalprinciplesinmathematicalphysicsgeometryandeconomicsqualitativeanalysisofnonlinearequationsandunilateralproblems |