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Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications [[electronic resource] /] / Yihong Du
| Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications [[electronic resource] /] / Yihong Du |
| Autore | Du Yihong <jin shi 1761.> |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 515.353 |
| Collana | Series on partial differential equations and applications |
| Soggetto topico |
Differential equations, Nonlinear - Numerical solutions
Differential equations, Partial - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-91949-7
9786611919498 981-277-444-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Preface ; 1. Krein-Rutman Theorem and the Principal Eigenvalue ; 2. Maximum Principles Revisited ; 2.1 Equivalent forms of the maximum principle ; 2.2 Maximum principle in W2N(O) ; 3. The Moving Plane Method ; 3.1 Symmetry over bounded domains
3.2 Symmetry over the entire space 3.3 Positivity of nonnegative solutions ; 4. The Method of Upper and Lower Solutions ; 4.1 Classical upper and lower solutions ; 4.2 Weak upper and lower solutions ; 5. The Logistic Equation ; 5.1 The classical case 5.2 The degenerate logistic equation 5.3 Perturbation and profile of solutions ; 6. Boundary Blow-Up Problems ; 6.1 The Keller-Osserman result and its generalizations ; 6.2 Blow-up rate and uniqueness ; 6.3 Logistic type equations with weights 7. Symmetry and Liouville Type Results over Half and Entire Spaces 7.1 Symmetry in a half space without strong maximum principle ; 7.2 Uniqueness results of logistic type equations over RN ; 7.3 Partial symmetry in the entire space ; 7.4 Some Liouville type results Appendix A Basic Theory of Elliptic Equations A.l Schauder theory for elliptic equations ; A.2 Sobolev spaces ; A.3 Weak solutions of elliptic equations ; A.4 LP theory of elliptic equations ; A.5 Maximum principles for elliptic equations ; A.5.1 The classical maximum principles A.5.2 Maximum principles and Harnack inequality for weak solutions |
| Record Nr. | UNINA-9910451406103321 |
Du Yihong <jin shi 1761.>
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications [[electronic resource] /] / Yihong Du
| Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications [[electronic resource] /] / Yihong Du |
| Autore | Du Yihong <jin shi 1761.> |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 515.353 |
| Collana | Series on partial differential equations and applications |
| Soggetto topico |
Differential equations, Nonlinear - Numerical solutions
Differential equations, Partial - Numerical solutions |
| ISBN |
1-281-91949-7
9786611919498 981-277-444-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Preface ; 1. Krein-Rutman Theorem and the Principal Eigenvalue ; 2. Maximum Principles Revisited ; 2.1 Equivalent forms of the maximum principle ; 2.2 Maximum principle in W2N(O) ; 3. The Moving Plane Method ; 3.1 Symmetry over bounded domains
3.2 Symmetry over the entire space 3.3 Positivity of nonnegative solutions ; 4. The Method of Upper and Lower Solutions ; 4.1 Classical upper and lower solutions ; 4.2 Weak upper and lower solutions ; 5. The Logistic Equation ; 5.1 The classical case 5.2 The degenerate logistic equation 5.3 Perturbation and profile of solutions ; 6. Boundary Blow-Up Problems ; 6.1 The Keller-Osserman result and its generalizations ; 6.2 Blow-up rate and uniqueness ; 6.3 Logistic type equations with weights 7. Symmetry and Liouville Type Results over Half and Entire Spaces 7.1 Symmetry in a half space without strong maximum principle ; 7.2 Uniqueness results of logistic type equations over RN ; 7.3 Partial symmetry in the entire space ; 7.4 Some Liouville type results Appendix A Basic Theory of Elliptic Equations A.l Schauder theory for elliptic equations ; A.2 Sobolev spaces ; A.3 Weak solutions of elliptic equations ; A.4 LP theory of elliptic equations ; A.5 Maximum principles for elliptic equations ; A.5.1 The classical maximum principles A.5.2 Maximum principles and Harnack inequality for weak solutions |
| Record Nr. | UNINA-9910777018603321 |
|
Du Yihong <jin shi 1761.>
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications / / Yihong Du
| Order structure and topological methods in nonlinear partial differential equations . Volume 1 Maximum principles and applications / / Yihong Du |
| Autore | Du Yihong <jin shi 1761.> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; Hackensack, NJ, : World Scientific, c2006 |
| Descrizione fisica | 1 online resource (202 p.) |
| Disciplina | 515.353 |
| Collana | Series on partial differential equations and applications |
| Soggetto topico |
Differential equations, Nonlinear - Numerical solutions
Differential equations, Partial - Numerical solutions |
| ISBN |
1-281-91949-7
9786611919498 981-277-444-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents ; Preface ; 1. Krein-Rutman Theorem and the Principal Eigenvalue ; 2. Maximum Principles Revisited ; 2.1 Equivalent forms of the maximum principle ; 2.2 Maximum principle in W2N(O) ; 3. The Moving Plane Method ; 3.1 Symmetry over bounded domains
3.2 Symmetry over the entire space 3.3 Positivity of nonnegative solutions ; 4. The Method of Upper and Lower Solutions ; 4.1 Classical upper and lower solutions ; 4.2 Weak upper and lower solutions ; 5. The Logistic Equation ; 5.1 The classical case 5.2 The degenerate logistic equation 5.3 Perturbation and profile of solutions ; 6. Boundary Blow-Up Problems ; 6.1 The Keller-Osserman result and its generalizations ; 6.2 Blow-up rate and uniqueness ; 6.3 Logistic type equations with weights 7. Symmetry and Liouville Type Results over Half and Entire Spaces 7.1 Symmetry in a half space without strong maximum principle ; 7.2 Uniqueness results of logistic type equations over RN ; 7.3 Partial symmetry in the entire space ; 7.4 Some Liouville type results Appendix A Basic Theory of Elliptic Equations A.l Schauder theory for elliptic equations ; A.2 Sobolev spaces ; A.3 Weak solutions of elliptic equations ; A.4 LP theory of elliptic equations ; A.5 Maximum principles for elliptic equations ; A.5.1 The classical maximum principles A.5.2 Maximum principles and Harnack inequality for weak solutions |
| Record Nr. | UNINA-9910813682203321 |
|
Du Yihong <jin shi 1761.>
|
||
| Singapore ; ; Hackensack, NJ, : World Scientific, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||