Zhitao Zhang
Variational, Topological, and Partial Order Methods with Their Applications
Zhitao Zhang
Variational, Topological, and Partial Order Methods with Their Applications
- Broschiertes Buch
- Merkliste
- Auf die Merkliste
- Bewerten Bewerten
- Teilen
- Produkt teilen
- Produkterinnerung
- Produkterinnerung
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 interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also…mehr
Andere Kunden interessierten sich auch für
- Zhitao ZhangVariational, Topological, and Partial Order Methods with Their Applications74,99 €
- Viorel BarbuNonlinear Differential Equations of Monotone Types in Banach Spaces74,99 €
- Viorel BarbuNonlinear Differential Equations of Monotone Types in Banach Spaces74,99 €
- Mark ElinNumerical Range of Holomorphic Mappings and Applications63,99 €
- Maciej BorodzikProblems on Partial Differential Equations48,99 €
- N. U. AhmedMeasure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control95,99 €
- Functional Analysis in Interdisciplinary Applications¿II110,99 €
-
-
-
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 interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Produktdetails
- Produktdetails
- Developments in Mathematics 29
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-642-42715-2
- 2013
- Seitenzahl: 344
- Erscheinungstermin: 15. Oktober 2014
- Englisch
- Abmessung: 235mm x 155mm x 19mm
- Gewicht: 528g
- ISBN-13: 9783642427152
- ISBN-10: 3642427154
- Artikelnr.: 41649909
- Developments in Mathematics 29
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-642-42715-2
- 2013
- Seitenzahl: 344
- Erscheinungstermin: 15. Oktober 2014
- Englisch
- Abmessung: 235mm x 155mm x 19mm
- Gewicht: 528g
- ISBN-13: 9783642427152
- ISBN-10: 3642427154
- Artikelnr.: 41649909
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-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( ) versus C01( ) 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.- Schrödinger systems from Bose-Einstein condensate.- Bibliography.
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-Amp ère 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 R N.- 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.- W 0 1, p(Ω) versus C 0 1(Ω) 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.- Schrödinger systems from Bose-Einstein condensate.- Bibliography.
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-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( ) versus C01( ) 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.- Schrödinger systems from Bose-Einstein condensate.- Bibliography.
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-Amp ère 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 R N.- 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.- W 0 1, p(Ω) versus C 0 1(Ω) 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.- Schrödinger systems from Bose-Einstein condensate.- Bibliography.