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Variational, topological, and partial order methods with their applications

Author: Zhitao Zhang
Publisher: Berlin : Springer, 2013.
Series: Developments in mathematics, 29.
Edition/Format:   Print book : EnglishView all editions and formats
Publication:Variational, Topological, and Partial Order Methods with Their Applications.
Database:WorldCat
Summary:

Covering leading-edge research, and with a focus on new developments in non-linear functional analysis, this is a vital addition to the literature that details theory as well as applications,  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Zhitao Zhang
ISBN: 9783642307089 3642307086 9783642307096 3642307094
OCLC Number: 819622808
In: Zhang, Zhitao
Description: 330 S : Ill.
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-Ampere 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-Fucik Spectrum.- The spectrum of a self-adjoint operator.- Dancer-Fucik Spectrum on bounded domains.- Dancer-Fucik point spectrum on RN.- Dancer-Fucik 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(OMEGA) versus C01(OMEGA ) 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.- Schrodinger systems from Bose-Einstein condensate.- Bibliography.
Series Title: Developments in mathematics, 29.
Responsibility: Zhitao Zhang.
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