Global Solution Curves for Semilinear Elliptic Equations.:
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore :
World Scientific,
2012.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results. |
| Beschreibung: | 1 online resource (254 pages) |
| Bibliographie: | Includes bibliographical references (pages 231-241). |
| ISBN: | 9789814374354 9814374350 9789814374347 9814374342 1280669756 9781280669750 9786613646682 6613646687 |
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| 245 | 1 | 0 | |a Global Solution Curves for Semilinear Elliptic Equations. |
| 260 | |a Singapore : |b World Scientific, |c 2012. | ||
| 300 | |a 1 online resource (254 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 505 | 0 | |a Preface; Contents; 1. Curves of Solutions on General Domains; 1.1 Continuation of solutions; 1.2 Symmetric domains in R2; 1.3 Turning points and the Morse index; 1.4 Convex domains in R2; 1.5 Pohozaev's identity and non-existence of solutions for elliptic systems; 1.5.1 Non-existence of solutions in the presence of supercritical and lower order terms; 1.5.2 Non-existence of solutions for a class of systems; 1.5.3 Pohozhaev's identity for a version of p-Laplace equation; 1.6 Problems at resonance; 2. Curves of Solutions on Balls; 2.1 Preliminary results. | |
| 505 | 8 | |a 2.2 Positivity of solution to the linearized problem2.3 Uniqueness of the solution curve; 2.4 Direction of a turn and exact multiplicity; 2.5 On a class of concave-convex equations; 2.6 Monotone separation of graphs; 2.7 The case of polynomial f(u) in two dimensions; 2.8 The case when f(0) <0; 2.9 Symmetry breaking; 2.10 Special equations; 2.11 Oscillations of the solution curve; 2.11.1 Asymptotics of some oscillatory integrals; 2.11.2 Reduction to the oscillatory integrals; 2.12 Uniqueness for non-autonomous problems; 2.12.1 Radial symmetry for the linearized equation. | |
| 505 | 8 | |a 2.13 Exact multiplicity for non-autonomous problems2.14 Numerical computation of solutions; 2.14.1 Using power series approximation; 2.14.2 Application to singular solutions; 2.15 Radial solutions of Neumann problem; 2.15.1 A computer assisted study of ground state solutions; 2.16 Global solution curves for a class of elliptic systems; 2.16.1 Preliminary results; 2.16.2 Global solution curves for Hamiltonian systems; 2.16.3 A class of special systems; 2.17 The case of a "thin" annulus; 2.18 A class of p-Laplace problems; 3. Two Point Boundary Value Problems. | |
| 505 | 8 | |a 3.1 Positive solutions of autonomous problems3.2 Direction of the turn; 3.3 Stability and instability of solutions; 3.3.1 S-shaped curves of combustion theory; 3.3.2 An extension of the stability condition; 3.4 S-shaped solution curves; 3.5 Computing the location and the direction of bifurcation; 3.5.1 Sign changing solutions; 3.6 A class of symmetric nonlinearities; 3.7 General nonlinearities; 3.8 Infinitely many curves with pitchfork bifurcation; 3.9 An oscillatory bifurcation from zero: A model example; 3.10 Exact multiplicity for Hamiltonian systems; 3.11 Clamped elastic beam equation. | |
| 505 | 8 | |a 3.11.1 Preliminary results3.11.2 Exact multiplicity of solutions; 3.12 Steady states of convective equations; 3.13 Quasilinear boundary value problems; 3.13.1 Numerical computations for the prescribed mean curvature equation; 3.14 The time map for quasilinear equations; 3.15 Uniqueness for a p-Laplace case; Bibliography. | |
| 520 | |a This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 231-241). | ||
| 546 | |a English. | ||
| 650 | 0 | |a Differential equations, Elliptic. |0 http://id.loc.gov/authorities/subjects/sh85037895 | |
| 650 | 0 | |a Mathematical analysis. |0 http://id.loc.gov/authorities/subjects/sh85082116 | |
| 650 | 6 | |a Équations différentielles elliptiques. | |
| 650 | 6 | |a Analyse mathématique. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Elliptic |2 fast | |
| 650 | 7 | |a Mathematical analysis |2 fast | |
| 758 | |i has work: |a Global solution curves for semilinear elliptic equations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGXWTJJ9C3DcTtpq6PWMj3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Korman, Philip. |t Global Solution Curves for Semilinear Elliptic Equations. |d Singapore : World Scientific, ©2012 |z 9789814374347 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn794328379 |
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| author | Korman, Philip, 1951- |
| author_GND | http://id.loc.gov/authorities/names/no2012096512 |
| author_facet | Korman, Philip, 1951- |
| author_role | |
| author_sort | Korman, Philip, 1951- |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA374 |
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| callnumber-search | QA374 .K384 2012 |
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| contents | Preface; Contents; 1. Curves of Solutions on General Domains; 1.1 Continuation of solutions; 1.2 Symmetric domains in R2; 1.3 Turning points and the Morse index; 1.4 Convex domains in R2; 1.5 Pohozaev's identity and non-existence of solutions for elliptic systems; 1.5.1 Non-existence of solutions in the presence of supercritical and lower order terms; 1.5.2 Non-existence of solutions for a class of systems; 1.5.3 Pohozhaev's identity for a version of p-Laplace equation; 1.6 Problems at resonance; 2. Curves of Solutions on Balls; 2.1 Preliminary results. 2.2 Positivity of solution to the linearized problem2.3 Uniqueness of the solution curve; 2.4 Direction of a turn and exact multiplicity; 2.5 On a class of concave-convex equations; 2.6 Monotone separation of graphs; 2.7 The case of polynomial f(u) in two dimensions; 2.8 The case when f(0) <0; 2.9 Symmetry breaking; 2.10 Special equations; 2.11 Oscillations of the solution curve; 2.11.1 Asymptotics of some oscillatory integrals; 2.11.2 Reduction to the oscillatory integrals; 2.12 Uniqueness for non-autonomous problems; 2.12.1 Radial symmetry for the linearized equation. 2.13 Exact multiplicity for non-autonomous problems2.14 Numerical computation of solutions; 2.14.1 Using power series approximation; 2.14.2 Application to singular solutions; 2.15 Radial solutions of Neumann problem; 2.15.1 A computer assisted study of ground state solutions; 2.16 Global solution curves for a class of elliptic systems; 2.16.1 Preliminary results; 2.16.2 Global solution curves for Hamiltonian systems; 2.16.3 A class of special systems; 2.17 The case of a "thin" annulus; 2.18 A class of p-Laplace problems; 3. Two Point Boundary Value Problems. 3.1 Positive solutions of autonomous problems3.2 Direction of the turn; 3.3 Stability and instability of solutions; 3.3.1 S-shaped curves of combustion theory; 3.3.2 An extension of the stability condition; 3.4 S-shaped solution curves; 3.5 Computing the location and the direction of bifurcation; 3.5.1 Sign changing solutions; 3.6 A class of symmetric nonlinearities; 3.7 General nonlinearities; 3.8 Infinitely many curves with pitchfork bifurcation; 3.9 An oscillatory bifurcation from zero: A model example; 3.10 Exact multiplicity for Hamiltonian systems; 3.11 Clamped elastic beam equation. 3.11.1 Preliminary results3.11.2 Exact multiplicity of solutions; 3.12 Steady states of convective equations; 3.13 Quasilinear boundary value problems; 3.13.1 Numerical computations for the prescribed mean curvature equation; 3.14 The time map for quasilinear equations; 3.15 Uniqueness for a p-Laplace case; Bibliography. |
| ctrlnum | (OCoLC)794328379 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Curves of Solutions on General Domains; 1.1 Continuation of solutions; 1.2 Symmetric domains in R2; 1.3 Turning points and the Morse index; 1.4 Convex domains in R2; 1.5 Pohozaev's identity and non-existence of solutions for elliptic systems; 1.5.1 Non-existence of solutions in the presence of supercritical and lower order terms; 1.5.2 Non-existence of solutions for a class of systems; 1.5.3 Pohozhaev's identity for a version of p-Laplace equation; 1.6 Problems at resonance; 2. Curves of Solutions on Balls; 2.1 Preliminary results.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.2 Positivity of solution to the linearized problem2.3 Uniqueness of the solution curve; 2.4 Direction of a turn and exact multiplicity; 2.5 On a class of concave-convex equations; 2.6 Monotone separation of graphs; 2.7 The case of polynomial f(u) in two dimensions; 2.8 The case when f(0) <0; 2.9 Symmetry breaking; 2.10 Special equations; 2.11 Oscillations of the solution curve; 2.11.1 Asymptotics of some oscillatory integrals; 2.11.2 Reduction to the oscillatory integrals; 2.12 Uniqueness for non-autonomous problems; 2.12.1 Radial symmetry for the linearized equation.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.13 Exact multiplicity for non-autonomous problems2.14 Numerical computation of solutions; 2.14.1 Using power series approximation; 2.14.2 Application to singular solutions; 2.15 Radial solutions of Neumann problem; 2.15.1 A computer assisted study of ground state solutions; 2.16 Global solution curves for a class of elliptic systems; 2.16.1 Preliminary results; 2.16.2 Global solution curves for Hamiltonian systems; 2.16.3 A class of special systems; 2.17 The case of a "thin" annulus; 2.18 A class of p-Laplace problems; 3. Two Point Boundary Value Problems.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.1 Positive solutions of autonomous problems3.2 Direction of the turn; 3.3 Stability and instability of solutions; 3.3.1 S-shaped curves of combustion theory; 3.3.2 An extension of the stability condition; 3.4 S-shaped solution curves; 3.5 Computing the location and the direction of bifurcation; 3.5.1 Sign changing solutions; 3.6 A class of symmetric nonlinearities; 3.7 General nonlinearities; 3.8 Infinitely many curves with pitchfork bifurcation; 3.9 An oscillatory bifurcation from zero: A model example; 3.10 Exact multiplicity for Hamiltonian systems; 3.11 Clamped elastic beam equation.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.11.1 Preliminary results3.11.2 Exact multiplicity of solutions; 3.12 Steady states of convective equations; 3.13 Quasilinear boundary value problems; 3.13.1 Numerical computations for the prescribed mean curvature equation; 3.14 The time map for quasilinear equations; 3.15 Uniqueness for a p-Laplace case; Bibliography.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. 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| id | ZDB-4-EBA-ocn794328379 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:24Z |
| institution | BVB |
| isbn | 9789814374354 9814374350 9789814374347 9814374342 1280669756 9781280669750 9786613646682 6613646687 |
| language | English |
| lccn | 2011278922 |
| oclc_num | 794328379 |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (254 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Korman, Philip, 1951- https://id.oclc.org/worldcat/entity/E39PCjJHxvFxTrjJDGV6xvVFqP http://id.loc.gov/authorities/names/no2012096512 Global Solution Curves for Semilinear Elliptic Equations. Singapore : World Scientific, 2012. 1 online resource (254 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Preface; Contents; 1. Curves of Solutions on General Domains; 1.1 Continuation of solutions; 1.2 Symmetric domains in R2; 1.3 Turning points and the Morse index; 1.4 Convex domains in R2; 1.5 Pohozaev's identity and non-existence of solutions for elliptic systems; 1.5.1 Non-existence of solutions in the presence of supercritical and lower order terms; 1.5.2 Non-existence of solutions for a class of systems; 1.5.3 Pohozhaev's identity for a version of p-Laplace equation; 1.6 Problems at resonance; 2. Curves of Solutions on Balls; 2.1 Preliminary results. 2.2 Positivity of solution to the linearized problem2.3 Uniqueness of the solution curve; 2.4 Direction of a turn and exact multiplicity; 2.5 On a class of concave-convex equations; 2.6 Monotone separation of graphs; 2.7 The case of polynomial f(u) in two dimensions; 2.8 The case when f(0) <0; 2.9 Symmetry breaking; 2.10 Special equations; 2.11 Oscillations of the solution curve; 2.11.1 Asymptotics of some oscillatory integrals; 2.11.2 Reduction to the oscillatory integrals; 2.12 Uniqueness for non-autonomous problems; 2.12.1 Radial symmetry for the linearized equation. 2.13 Exact multiplicity for non-autonomous problems2.14 Numerical computation of solutions; 2.14.1 Using power series approximation; 2.14.2 Application to singular solutions; 2.15 Radial solutions of Neumann problem; 2.15.1 A computer assisted study of ground state solutions; 2.16 Global solution curves for a class of elliptic systems; 2.16.1 Preliminary results; 2.16.2 Global solution curves for Hamiltonian systems; 2.16.3 A class of special systems; 2.17 The case of a "thin" annulus; 2.18 A class of p-Laplace problems; 3. Two Point Boundary Value Problems. 3.1 Positive solutions of autonomous problems3.2 Direction of the turn; 3.3 Stability and instability of solutions; 3.3.1 S-shaped curves of combustion theory; 3.3.2 An extension of the stability condition; 3.4 S-shaped solution curves; 3.5 Computing the location and the direction of bifurcation; 3.5.1 Sign changing solutions; 3.6 A class of symmetric nonlinearities; 3.7 General nonlinearities; 3.8 Infinitely many curves with pitchfork bifurcation; 3.9 An oscillatory bifurcation from zero: A model example; 3.10 Exact multiplicity for Hamiltonian systems; 3.11 Clamped elastic beam equation. 3.11.1 Preliminary results3.11.2 Exact multiplicity of solutions; 3.12 Steady states of convective equations; 3.13 Quasilinear boundary value problems; 3.13.1 Numerical computations for the prescribed mean curvature equation; 3.14 The time map for quasilinear equations; 3.15 Uniqueness for a p-Laplace case; Bibliography. This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results. Print version record. Includes bibliographical references (pages 231-241). English. Differential equations, Elliptic. http://id.loc.gov/authorities/subjects/sh85037895 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Équations différentielles elliptiques. Analyse mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations, Elliptic fast Mathematical analysis fast has work: Global solution curves for semilinear elliptic equations (Text) https://id.oclc.org/worldcat/entity/E39PCGXWTJJ9C3DcTtpq6PWMj3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Korman, Philip. Global Solution Curves for Semilinear Elliptic Equations. Singapore : World Scientific, ©2012 9789814374347 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=457181 Volltext |
| spellingShingle | Korman, Philip, 1951- Global Solution Curves for Semilinear Elliptic Equations. Preface; Contents; 1. Curves of Solutions on General Domains; 1.1 Continuation of solutions; 1.2 Symmetric domains in R2; 1.3 Turning points and the Morse index; 1.4 Convex domains in R2; 1.5 Pohozaev's identity and non-existence of solutions for elliptic systems; 1.5.1 Non-existence of solutions in the presence of supercritical and lower order terms; 1.5.2 Non-existence of solutions for a class of systems; 1.5.3 Pohozhaev's identity for a version of p-Laplace equation; 1.6 Problems at resonance; 2. Curves of Solutions on Balls; 2.1 Preliminary results. 2.2 Positivity of solution to the linearized problem2.3 Uniqueness of the solution curve; 2.4 Direction of a turn and exact multiplicity; 2.5 On a class of concave-convex equations; 2.6 Monotone separation of graphs; 2.7 The case of polynomial f(u) in two dimensions; 2.8 The case when f(0) <0; 2.9 Symmetry breaking; 2.10 Special equations; 2.11 Oscillations of the solution curve; 2.11.1 Asymptotics of some oscillatory integrals; 2.11.2 Reduction to the oscillatory integrals; 2.12 Uniqueness for non-autonomous problems; 2.12.1 Radial symmetry for the linearized equation. 2.13 Exact multiplicity for non-autonomous problems2.14 Numerical computation of solutions; 2.14.1 Using power series approximation; 2.14.2 Application to singular solutions; 2.15 Radial solutions of Neumann problem; 2.15.1 A computer assisted study of ground state solutions; 2.16 Global solution curves for a class of elliptic systems; 2.16.1 Preliminary results; 2.16.2 Global solution curves for Hamiltonian systems; 2.16.3 A class of special systems; 2.17 The case of a "thin" annulus; 2.18 A class of p-Laplace problems; 3. Two Point Boundary Value Problems. 3.1 Positive solutions of autonomous problems3.2 Direction of the turn; 3.3 Stability and instability of solutions; 3.3.1 S-shaped curves of combustion theory; 3.3.2 An extension of the stability condition; 3.4 S-shaped solution curves; 3.5 Computing the location and the direction of bifurcation; 3.5.1 Sign changing solutions; 3.6 A class of symmetric nonlinearities; 3.7 General nonlinearities; 3.8 Infinitely many curves with pitchfork bifurcation; 3.9 An oscillatory bifurcation from zero: A model example; 3.10 Exact multiplicity for Hamiltonian systems; 3.11 Clamped elastic beam equation. 3.11.1 Preliminary results3.11.2 Exact multiplicity of solutions; 3.12 Steady states of convective equations; 3.13 Quasilinear boundary value problems; 3.13.1 Numerical computations for the prescribed mean curvature equation; 3.14 The time map for quasilinear equations; 3.15 Uniqueness for a p-Laplace case; Bibliography. Differential equations, Elliptic. http://id.loc.gov/authorities/subjects/sh85037895 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Équations différentielles elliptiques. Analyse mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations, Elliptic fast Mathematical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037895 http://id.loc.gov/authorities/subjects/sh85082116 |
| title | Global Solution Curves for Semilinear Elliptic Equations. |
| title_auth | Global Solution Curves for Semilinear Elliptic Equations. |
| title_exact_search | Global Solution Curves for Semilinear Elliptic Equations. |
| title_full | Global Solution Curves for Semilinear Elliptic Equations. |
| title_fullStr | Global Solution Curves for Semilinear Elliptic Equations. |
| title_full_unstemmed | Global Solution Curves for Semilinear Elliptic Equations. |
| title_short | Global Solution Curves for Semilinear Elliptic Equations. |
| title_sort | global solution curves for semilinear elliptic equations |
| topic | Differential equations, Elliptic. http://id.loc.gov/authorities/subjects/sh85037895 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Équations différentielles elliptiques. Analyse mathématique. MATHEMATICS Differential Equations General. bisacsh Differential equations, Elliptic fast Mathematical analysis fast |
| topic_facet | Differential equations, Elliptic. Mathematical analysis. Équations différentielles elliptiques. Analyse mathématique. MATHEMATICS Differential Equations General. Differential equations, Elliptic Mathematical analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=457181 |
| work_keys_str_mv | AT kormanphilip globalsolutioncurvesforsemilinearellipticequations |