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...
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| Corporate Author: | |
| Format: | Electronic |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2013.
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| Series: | Developments in Mathematics,
29 |
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-30709-6 |
Table of Contents:
- 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-Ampr̈e 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-Fu ik Spectrum
- The spectrum of a self-adjoint operator
- Dancer-Fu ik Spectrum on bounded domains
- Dancer-Fu ik point spectrum on RN
- Dancer-Fu ik 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(♭<U+0004>) local minimizers
- Multiplicity results for the quasilinear problems
- Uniqueness results
- 10 Nonlocal Kirchhoff Elliptic Problems
- Introduction
- Yang index and critical groups to nonlocal problems
- Variational methods and invariant sets of descent flow
- Uniqueness of solution for a class of Kirchhoff-type equations
- 11 Free Boundary Problems, System of equations for Bose-Einstein Condensate and Competing Species
- Competing system with many species
- Optimal partition problems
- Schrd̲inger systems from Bose-Einstein condensate
- Bibliography.