Entire solutions of semilinear elliptic equations
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Basel ; Boston ; Berlin
Birkhäuser
1997
|
| Schriftenreihe: | Progress in nonlinear differential equations and their applications
33 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Kuzin, Il'ja A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Entire solutions of semilinear elliptic equations |c I. Kuzin ; S. Pohozaev |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 1997 | |
| 300 | |a VI, 250 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in nonlinear differential equations and their applications |v 33 | |
| 650 | 7 | |a Equations de réaction-diffusion |2 ram | |
| 650 | 7 | |a Equations différentielles elliptiques |2 ram | |
| 650 | 7 | |a Physique mathématique |2 ram | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Differential equations, Elliptic | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Reaction-diffusion equations | |
| 650 | 0 | 7 | |a Semilineare elliptische Differentialgleichung |0 (DE-588)4225683-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Semilineare elliptische Differentialgleichung |0 (DE-588)4225683-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pochožaev, Stanislav I. |d 1935- |e Verfasser |0 (DE-588)129018880 |4 aut | |
| 830 | 0 | |a Progress in nonlinear differential equations and their applications |v 33 |w (DE-604)BV007934389 |9 33 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007737579 | ||
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 355f 2001 A 21717 |
|---|---|
| DE-BY-TUM_katkey | 863452 |
| DE-BY-TUM_media_number | 040020189255 |
| _version_ | 1816711775128649728 |
| adam_text | Contents
Introduction 1
§ 0 Notation 4
Chapter 1
Classical Variational Method 5
§ 1 Preliminaries 5
§ 2 The Classical Method: Absolute Minimum 12
§ 3 Approximation by Bounded Domains 27
§ 4 Approximation for Problems on an Absolute Minimum 32
§ 5 The Monotonicity Method. Uniqueness of Solutions 36
Chapter 2
Variational Methods for Eigenvalue Problems 39
§ 6 Abstract Theorems 39
§ 7 The Equation Aw + a(x) u p 2u A6(x)|u|9 2w = 0 47
§ 8 Radial Solutions 55
§ 9 The Equation Au + Xf(u) = 0 58
§ 10 The Equation Au A|u|p 2u b(x) u i 2u = 0 67
§ 11 The Comparison Method for Eigenvalue Problems
(Concentration Compactness) 72
§ 12 Homogeneous Problems 81
Chapter 3
Special Variational Methods 83
§ 13 The Mountain Pass Method 83
§ 14 Behavior of PS sequences. The Concentration Compactness
(Comparison) Method 90
§ 15 A General Comparison Theorem. The Ground State.
Examples for the Mountain Pass Method 106
§ 16 Behavior of PS sequences in the Symmetric Case.
Existence Theorems 113
§ 17 Nonradial Solutions of Radial Equations 120
§ 18 Methods of Bounded Domains Approximation 124
vi Contents
Chapter 4
Radial Solutions: The ODE Method 129
§ 19 Basic Techniques of the ODE Method 129
§ 20 Autonomous Equations in the iV dimensional Case 132
§ 21 Decaying Solutions. The One dimensional Case 138
§ 22 The Phase Plane Method. The Emden Fowler Equation 141
§ 23 Scaling 153
§ 24 Positive Solutions. The Shooting Method 154
Chapter 5
Other Methods 159
§ 25 The Method of Upper and Lower Solutions 159
§ 26 The Leray Schauder Method 171
§ 27 The Method of A Priori Estimates 175
§ 28 The Fibering Method. Existence of Infinitely Many Solutions 205
§ 29 Nonexistence Results 217
Appendices 223
A Spaces and Functionals 223
B The Strauss Lemma 226
C Invariant Spaces 228
D The Schwarz Rearrangement 230
E The Mountain Pass Method 234
References 243
Index 249
|
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| author | Kuzin, Il'ja A. Pochožaev, Stanislav I. 1935- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011497572 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:14:19Z |
| institution | BVB |
| isbn | 3764353236 0817653236 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007737579 |
| oclc_num | 37426447 |
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| physical | VI, 250 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in nonlinear differential equations and their applications |
| series2 | Progress in nonlinear differential equations and their applications |
| spellingShingle | Kuzin, Il'ja A. Pochožaev, Stanislav I. 1935- Entire solutions of semilinear elliptic equations Progress in nonlinear differential equations and their applications Equations de réaction-diffusion ram Equations différentielles elliptiques ram Physique mathématique ram Mathematische Physik Differential equations, Elliptic Mathematical physics Reaction-diffusion equations Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| subject_GND | (DE-588)4225683-5 |
| title | Entire solutions of semilinear elliptic equations |
| title_auth | Entire solutions of semilinear elliptic equations |
| title_exact_search | Entire solutions of semilinear elliptic equations |
| title_full | Entire solutions of semilinear elliptic equations I. Kuzin ; S. Pohozaev |
| title_fullStr | Entire solutions of semilinear elliptic equations I. Kuzin ; S. Pohozaev |
| title_full_unstemmed | Entire solutions of semilinear elliptic equations I. Kuzin ; S. Pohozaev |
| title_short | Entire solutions of semilinear elliptic equations |
| title_sort | entire solutions of semilinear elliptic equations |
| topic | Equations de réaction-diffusion ram Equations différentielles elliptiques ram Physique mathématique ram Mathematische Physik Differential equations, Elliptic Mathematical physics Reaction-diffusion equations Semilineare elliptische Differentialgleichung (DE-588)4225683-5 gnd |
| topic_facet | Equations de réaction-diffusion Equations différentielles elliptiques Physique mathématique Mathematische Physik Differential equations, Elliptic Mathematical physics Reaction-diffusion equations Semilineare elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007737579&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV007934389 |
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