常微分方程基础理论（影印版）

图书标准信息

• 作者 [美]赫斯赫（Hsieh P.F.） 著
• 出版社 高等教育出版社
• 出版时间 2007-07
• 版次 1
• ISBN 9787040220667
• 定价 37.40元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 468页
• 字数 500千字
• 正文语种 英语
• 丛书 天元基金影印数学丛书

【内容简介】

　　本书为开展常微分方程研究工作的读者提供必要的准备知识，可作为本科高年级和研究生常微分方程课程教材。
　　本书内容分为四部分：第一部分(第一、二、三章)的内容包括解的存在性、唯一性、对数据的光滑依赖性，以及解的非唯一性；第二部分(第四、六、七章)讨论线性常微分方程，书中用矩阵的S-N分解代替Jordan分解，前者的计算较后者更容易；第三部分(第八、九、十章)讨论非线性常微分方程的稳定性、渐近稳定性等几何理论；第四部分(第五、十一，十二、十三章)讨论常微分方程的幂级数解，包括线性常微分方程的奇点分类及非线性常微分方程当参数或自变量趋向某奇点时的渐近解等。

【目录】

Preface
ChapterⅠ.FundamentalTheoremsofOrdinaryDifferentialEquations
Ⅰ-1.ExistenceanduniquenesswiththeLipschitzcondition
Ⅰ-2.ExistencewithouttheLipschitzcondition
Ⅰ-3.Someglobalpropertiesofsolutions
Ⅰ-4.Analyticdifferentialequations
ExercisesⅠ

ChapterⅡ.DependenceonData
Ⅱ-1.Continuitywithrespecttoinitialdataandparameters
Ⅱ-2.Differentiability
ExercisesⅡ

ChapterⅢ.Nonuniqueness
Ⅲ-1.Examples
Ⅲ-2.TheKnesertheorem
Ⅲ-3.SolutioncurvesontheboundaryofR（A)
Ⅲ-4.Maximalandminimalsolutions
Ⅲ-5.Acomparisontheorem
Ⅲ-6.Sufficientconditionsforuniqueness
ExercisesⅢ

ChapterⅣ.GeneralTheoryofLinearSystems
Ⅳ-1.Somebasicresultsconcerningmatrices
Ⅳ-2.Homogeneoussystemsoflineardifferentialequations
Ⅳ-3.Homogeneoussystemswithconstantcoefficients
Ⅳ-4.Systemswithperiodiccoefficients
Ⅳ-5.LinearHamiltoniansystemswithperiodiccoefficients
Ⅳ-6.Nonhomogeneousequations
Ⅳ-7.Higher-orderscalarequations
ExercisesⅣ

ChapterⅤ.SingularitiesoftheFirstKind
Ⅴ-1.Formalsolutionsofanalgebraicdifferentialequation
Ⅴ-2.Convergenceofformalsolutionsofasystemofthefirstkind
Ⅴ-3.TheS-Ndecompositionofamatrixofinfiniteorder
Ⅴ-4.TheS-Ndecompositionofadifferentialoperator
Ⅴ-5.Anormalformofadifferentialoperator
Ⅴ-6.Calculationofthenormalformofadifferentialoperator
Ⅴ-7.Classificationofsingularitiesofhomogeneouslinearsystems
ExercisesⅤ

ChapterⅥ.Boundary-ValueProblemsofLinearDifferentialEquationsoftheSecond-Order
Ⅵ-1.Zerosofsolutions
Ⅵ-2.Sturm-Liouvilleproblems
Ⅵ-3.Eigenvalueproblems
Ⅵ-4.Eigenfunctionexpansions
Ⅵ-5.Jostsolutions
Ⅵ-6.Scatteringdata
Ⅵ-7.Refiectionlesspotentials
Ⅵ-8.Constructionofapotentialforgivendata
Ⅵ-9.Differentialequationssatisfiedbyreflectionlesspotentials
Ⅵ-10.Periodicpotentials
ExercisesⅥ

ChapterⅦ.AsymptoticBehaviorofSolutionsofLinearSystems
Ⅶ-1.Liapounoffstypenumbers
Ⅶ-2.Liapounoffstypenumbersofahomogeneouslinearsystem
Ⅶ-3.CalculationofLiapounoffstypenumbersofsolutions
Ⅶ-4.Adiagonalizationtheorem
Ⅶ-5.Systemswithasymptoticallyconstantcoefficients
Ⅶ-6.AnapplicationoftheFloquettheorem
ExercisesⅦ

ChapterⅧ.Stability
Ⅷ-1.Basicdefinitions
Ⅷ-2.Asufficientconditionforasymptoticstability
Ⅷ-3.Stablemanifolds
Ⅷ-4.Analyticstructureofstablemanifolds
Ⅷ-5.Two-dimensionallinearsystemswithconstantcoefficients
Ⅷ-6.AnalyticsystemsinR2
Ⅷ-7.Perturbationsofanimpropernodeandasaddlepoint
Ⅷ-8.Perturbationsofapropernode
Ⅷ-9.Perturbationofaspiralpoint
Ⅷ-10.Perturbationofacenter
ExercisesⅧ

ChapterⅨ.AutonomousSystems
Ⅸ-1.Limit-invariantsets
Ⅸ-2.Liapounoffsdirectmethod
Ⅸ-3.Orbitalstability
Ⅸ-4.ThePoincare-Bendixsontheorem
Ⅸ-5.IndicesofJordancurves
ExercisesⅨ

ChapterⅩ.TheSecond-OrderDifferentialEquation（d2x)/（dt2)+h（x)*（dx)/（dt)+g（x)=0
Ⅹ-1.Two-pointboundary-valueproblems
Ⅹ-2.ApplicationsoftheLiapounofffunctions
Ⅹ-3.Existenceanduniquenessofperiodicorbits
Ⅹ-4.MultipliersoftheperiodicorbitofthevanderPolequation
Ⅹ-5.ThevanderPolequationforasmallε>0
Ⅹ-6.ThevanderPolequationforalargeparameter
Ⅹ-7.AtheoremduetoM.Nagumo
Ⅹ-8.Asingularperturbationproblem
ExercisesⅩ

ChapterⅪ.AsymptoticExpansions
Ⅺ-1.AsymptoticexpansionsinthesenseofPoincare
Ⅺ-2.Gevreyasymptotics
Ⅺ-3.FlatfunctionsintheGevreyasymptotics
Ⅺ-4.BasicpropertiesofGevreyasymptoticexpansions
Ⅺ-5.ProofofLemmaⅪ-2-6
ExercisesⅪ

ChapterⅫ.AsymptoticExpansionsinaParameter
Ⅻ-1.Anexistencetheorem
Ⅻ-2.Basicestimates
Ⅻ-3.ProofofTheoremⅫ-1-2
Ⅻ-4.Ablock-diagonalizationtheorem
Ⅻ-5.Gevreyasymptoticsolutionsinaparameter
Ⅻ-6.Analyticsimplificationinaparameter
ExercisesⅫ

ChapterⅩⅢ.SingularitiesoftheSecondKind
ⅩⅢ-1.Anexistencetheorem
ⅩⅢ-2.Basicestimates
ⅩⅢ-3.ProofofTheoremⅩⅢ-1-2
ⅩⅢ-4.Ablock-diagonalizationtheorem
ⅩⅢ-5.Cyclicvectors（AlemmaofP.Deligne)
ⅩⅢ-6.TheHukuhara-Turrittintheorem
ⅩⅢ-7.Ann-th-orderlineardifferentialequationatasingularpointofthesecondkind
ⅩⅢ-8.Gevreypropertyofasymptoticsolutionsatanirregularsingularpoint
ExercisesⅩⅢ
References
Index