张恭庆的数学生活

图书标准信息

• 作者 张恭庆 著
• 出版社 世界图书出版公司
• 出版时间 2014-05
• 版次 1
• ISBN 9787510075933
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 439页
• 正文语种 英语
• 丛书 经典数学丛书

【内容简介】

　　Manynonlinearanalysisproblemshavetheirrootsingeometry，astronomy，fluidandelasticmechanics，physics，chemistry，biology，controltheory，imageprocessingandeconomics.Thetheoriesandmethodsinnonlinearanalysisstemfrommanyareasofmathematics：Ordinarydrfferentialequations，partialdifferentialequations，thecalculusofvariations，dynamicalsystems，differentialgeometry，Liegroups，algebraictopology，linearandnonlinearfunctionalanalysis，measuretheory，harmonicanalysis，convexanalysis，gametheory，optimizationtheory，etc.Amidstsolvingtheseproblems，manybranchesareintertwined，therebyadvancingeachother.
　　Thebookistheresultofmanyyearsofrevisionoftheauthor'slecturenotes.Someofthemoreinvolvedsectionswereoriginallyusedinseminarsasintroductorypartsofsomenewsubjects.However，duetotheirimportance，thematerialshavebeenreorganizedandsupplemented，sothattheymaybemorevaluabletothereaders.

【目录】

1Linearization
1.1DifferentialCalculusinBanachSpaces
1.1.1FrechetDerivativesandGateauxDerivatives
1.1.2NemytsckiOperator
1.1.3High-OrderDerivatives
1.2ImplicitFunctionTheoremandContinuityMethod
1.2.1InverseFunctionTheorem
1.2.2Applications
1.2.3ContinuityMethod
1.3Lyapunov-SchmidtReductionandBifurcation
1.3.1Bifurcation
1.3.2Lyapunov-SchmidtReduction
1.3.3APerturbationProblem
1.3.4Gluing
1.3.5Transversality
1.4HardImplicitFunctionTheorem
1.4.1TheSmallDivisorProblem
1.4.2Nash-MoserIteration

2Fixed-PointTheorems
2.1OrderMethod
2.2ConvexFunctionandItsSubdifferentials
2.2.1ConvexFunctions
2.2.2Subdifferentials
2.3ConvexityandCompactness
2.4NonexpansiveMaps
2.5MonotoneMappings
2.6MaximalMonotoneMapping

3DegreeTheoryandApplications
3.1TheNotionofTopologicalDegree
3.2FundamentalPropertiesandCalculationsofBrouwerDegrees
3.3ApplicationsofBrouwerDegree
3.3.1BrouwerFixed-PointTheorem
3.3.2TheBorsuk-UlamTheoremandItsConsequences
3.3.3DegreesforSlEquivariantMappings
3.3.4Intersection
3.4Leray-SchauderDegrees
3.5TheGlobalBifurcation
3.6Applications
3.6.1DegreeTheoryonClosedConvexSets,
3.6.2PositiveSolutionsandtheScalingMethod
3.6.3Krein-RutmanTheoryforPositiveLinearOperators
3.6.4MultipleSolutions
3.6.5AFreeBoundaryProblem
3.6.6Bridging
3.7Extensions
3.7.1Set-ValuedMappings
3.7.2StrictSetContractionMappingsandCondensingMappings
3.7.3FredholmMappings

4MinimizationMethods
4.1VariationalPrinciples
4.1.1ConstraintProblems
4.1.2Euler-LagrangeEquation
4.1.3DualVariationalPrinciple
4.2DirectMethod
4.2.1FundamentalPrinciple
4.2.2Examples
4.2.3ThePrescribingGaussianCurvatureProblemandtheSchwarzSymmetricRearrangement
4.3Quasi-Convexity
4.3.1WeakContinuityandQuasi-Convexity
4.3.2MorreyTheorem
4.3.3NonlinearElasticity
4.4RelaxationandYoungMeasure
4.4.1Relaxations
4.4.2YoungMeasure
4.5OtherFunctionSpaces
4.5.1BVSpace
4.5.2HardySpaceandBMOSpace
4.5.3CompensationCompactness
4.5.4ApplicationstotheCalculusofVariations
……
5TopologicalandVariationalMethods
Notes
References