An Introduction to Minimax Theorems and Their Applications to Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2001
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
52 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text is meant to be an introduction to critical point theory and its applications to differential equations. It is designed for graduate and postgraduate students as well as for specialists in the fields of differential equations, variational methods and optimization. Although related material can be the treatment here has the following main purposes: found in other books, - To present a survey on existing minimax theorems, - To give applications to elliptic differential equations in bounded domains and periodic second-order ordinary differential equations, - To consider the dual variational method for problems with continuous and discontinuous nonlinearities, - To present some elements of critical point theory for locally Lipschitz functionals and to give applications to fourth-order differential equations with discontinuous nonlinearities, - To study homo clinic solutions of differential equations via the variational method. The Contents of the book consist of seven chapters, each one divided into several sections. A bibliography is attached to the end of each chapter. In Chapter I, we present minimization theorems and the mountain-pass theorem of Ambrosetti-Rabinowitz and some of its extensions. The concept of differentiability of mappings in Banach spaces, the Fnkhet's and Gateaux derivatives, second-order derivatives and general minimization theorems, variational principles of Ekeland [Ekl] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais-Smale conditions and mountain-pass theorems are considered |
| Beschreibung: | 1 Online-Ressource (XII, 274 p) |
| ISBN: | 9781475733082 9781441948496 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/978-1-4757-3308-2 |
Internformat
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| 245 | 1 | 0 | |a An Introduction to Minimax Theorems and Their Applications to Differential Equations |c by Maria Rosário Grossinho, Stepan Agop Tersian |
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| 490 | 1 | |a Nonconvex Optimization and Its Applications |v 52 |x 1571-568X | |
| 500 | |a This text is meant to be an introduction to critical point theory and its applications to differential equations. It is designed for graduate and postgraduate students as well as for specialists in the fields of differential equations, variational methods and optimization. Although related material can be the treatment here has the following main purposes: found in other books, - To present a survey on existing minimax theorems, - To give applications to elliptic differential equations in bounded domains and periodic second-order ordinary differential equations, - To consider the dual variational method for problems with continuous and discontinuous nonlinearities, - To present some elements of critical point theory for locally Lipschitz functionals and to give applications to fourth-order differential equations with discontinuous nonlinearities, - To study homo clinic solutions of differential equations via the variational method. The Contents of the book consist of seven chapters, each one divided into several sections. A bibliography is attached to the end of each chapter. In Chapter I, we present minimization theorems and the mountain-pass theorem of Ambrosetti-Rabinowitz and some of its extensions. The concept of differentiability of mappings in Banach spaces, the Fnkhet's and Gateaux derivatives, second-order derivatives and general minimization theorems, variational principles of Ekeland [Ekl] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais-Smale conditions and mountain-pass theorems are considered | ||
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9781475733082 9781441948496 |
| issn | 1571-568X |
| language | English |
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| series | Nonconvex Optimization and Its Applications |
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| spelling | Rosário Grossinho, Maria Verfasser aut An Introduction to Minimax Theorems and Their Applications to Differential Equations by Maria Rosário Grossinho, Stepan Agop Tersian Boston, MA Springer US 2001 1 Online-Ressource (XII, 274 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 52 1571-568X This text is meant to be an introduction to critical point theory and its applications to differential equations. It is designed for graduate and postgraduate students as well as for specialists in the fields of differential equations, variational methods and optimization. Although related material can be the treatment here has the following main purposes: found in other books, - To present a survey on existing minimax theorems, - To give applications to elliptic differential equations in bounded domains and periodic second-order ordinary differential equations, - To consider the dual variational method for problems with continuous and discontinuous nonlinearities, - To present some elements of critical point theory for locally Lipschitz functionals and to give applications to fourth-order differential equations with discontinuous nonlinearities, - To study homo clinic solutions of differential equations via the variational method. The Contents of the book consist of seven chapters, each one divided into several sections. A bibliography is attached to the end of each chapter. In Chapter I, we present minimization theorems and the mountain-pass theorem of Ambrosetti-Rabinowitz and some of its extensions. The concept of differentiability of mappings in Banach spaces, the Fnkhet's and Gateaux derivatives, second-order derivatives and general minimization theorems, variational principles of Ekeland [Ekl] and Borwein & Preiss [BP] are proved and relations to the minimization problem are given. Deformation lemmata, Palais-Smale conditions and mountain-pass theorems are considered Mathematics Functional equations Functional analysis Differential equations, partial Mathematical optimization Partial Differential Equations Difference and Functional Equations Functional Analysis Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Mathematik Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Minimax-Theorem (DE-588)4135131-9 gnd rswk-swf Minimax-Theorem (DE-588)4135131-9 s Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Tersian, Stepan Agop Sonstige oth Nonconvex Optimization and Its Applications 52 (DE-604)BV010085908 52 https://doi.org/10.1007/978-1-4757-3308-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rosário Grossinho, Maria An Introduction to Minimax Theorems and Their Applications to Differential Equations Nonconvex Optimization and Its Applications Mathematics Functional equations Functional analysis Differential equations, partial Mathematical optimization Partial Differential Equations Difference and Functional Equations Functional Analysis Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Mathematik Differentialgleichung (DE-588)4012249-9 gnd Minimax-Theorem (DE-588)4135131-9 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4135131-9 |
| title | An Introduction to Minimax Theorems and Their Applications to Differential Equations |
| title_auth | An Introduction to Minimax Theorems and Their Applications to Differential Equations |
| title_exact_search | An Introduction to Minimax Theorems and Their Applications to Differential Equations |
| title_full | An Introduction to Minimax Theorems and Their Applications to Differential Equations by Maria Rosário Grossinho, Stepan Agop Tersian |
| title_fullStr | An Introduction to Minimax Theorems and Their Applications to Differential Equations by Maria Rosário Grossinho, Stepan Agop Tersian |
| title_full_unstemmed | An Introduction to Minimax Theorems and Their Applications to Differential Equations by Maria Rosário Grossinho, Stepan Agop Tersian |
| title_short | An Introduction to Minimax Theorems and Their Applications to Differential Equations |
| title_sort | an introduction to minimax theorems and their applications to differential equations |
| topic | Mathematics Functional equations Functional analysis Differential equations, partial Mathematical optimization Partial Differential Equations Difference and Functional Equations Functional Analysis Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Mathematik Differentialgleichung (DE-588)4012249-9 gnd Minimax-Theorem (DE-588)4135131-9 gnd |
| topic_facet | Mathematics Functional equations Functional analysis Differential equations, partial Mathematical optimization Partial Differential Equations Difference and Functional Equations Functional Analysis Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Mathematik Differentialgleichung Minimax-Theorem |
| url | https://doi.org/10.1007/978-1-4757-3308-2 |
| volume_link | (DE-604)BV010085908 |
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