Variational, Topological, and Partial Order Methods with Their Applications
Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and...
Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Livre numérique |
| Γλώσσα: | Anglais |
| Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Έκδοση: | 1st ed. 2013. |
| Σειρά: | Developments in Mathematics
29 |
| Διαθέσιμο Online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Σημείωση: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Variational, topological, and partial order methods with their applications, Zhitao Zhang, Heidelberg, Springer, 2013, 1 vol. (XI - 330 p. ), Developments in mathematics, 978-3-642-30708-9 |
Πίνακας περιεχομένων:
- 1 Preliminaries Sobolev spaces and embedding theorems Critical point Cone and partial order Brouwer Degree Compact map and Leray-Schauder Degree Fredholm operators Fixed point index Banach's Contract Theorem, Implicit Functions Theorem Krein-Rutman theorem Bifurcation theory Rearrangements of sets and functions Genus and Category Maximum principles and symmetry of solution Comparison theorems 2 Cone and Partial Order Methods Increasing operators Decreasing operators Mixed monotone operators Applications of mixed monotone operators Further results on cones and partial order methods 3 Minimax Methods Mountain Pass Theorem and Minimax Principle Linking Methods Local linking Methods 4 Bifurcation and Critical Point Introduction Main results with parameter Equations without the parameter 5 Solutions of a Class of Monge-Ampère Equations Introduction Moving plane argument Existence and non-existence results Bifurcation and the equation with a parameter Appendix 6 Topological Methods and Applications Superlinear system of integral equations and applications Existence of positive solutions for a semilinear elliptic system 7 Dancer-Fučik Spectrum The spectrum of a self-adjoint operator Dancer-Fučik Spectrum on bounded domains Dancer-Fučik point spectrum on RN Dancer-Fučik spectrum and asymptotically linear elliptic problems 8 Sign-changing Solutions Sign-changing solutions for superlinear Dirichlet problems Sign-changing solutions for jumping nonlinear problems 9 Extension of Brezis-Nirenberg's Results and Quasilinear Problems Introduction W01,p( ) versus C01(¯) local minimizers Multiplicity results for the quasilinear problems Uniqueness results