标题：带差分方程的振动性(英)
内容提要
Inthepresentmonograph,IhavecollectedsomeoftheresultswhichmycooperatorsandIhaveobtainedinthelastfewyears.Thebookisdividedintosevenchapters.Chapter1introducessomepreliminarymaterials,includingandsomeresultsfromcalculusoffinitedifferenceswhicharetakenfromthemonographofAgarwal(2000).Chapter2providessomeresultsintheoscillationoffirstorderdelaydifferenceequations.Chapter3discussesoscillation,nonoscillationandasymptoticclassificationofnonoscillatorysolutionsofsecondnonlineardifferenceequations.Chapter4investigatestheoscillationandexistenceofnonoscillatorysolutionsofhigherorderneutraldelaydifferenceequations.Chapter5dealswithoscillationfordelaydifferenceequationswithcontinuousvariables.Chapter6concernsoscillationandnonoscillationoffunctionalequations.Thelastchapter,Chapter7studiesoscillationandexistenceofnonoscillatorysolutionsofdelaypartialdifferenceequations.
编辑推荐
In the presentmonograph,IhavecollectedsomeoftheresultswhichmycooperatorsandIhaveobtainedinthelastfewyears.Thebookisdividedintosevenchapters.Chapter1introducessomepreliminarymaterials,includingandsomeresultsfromcalculusoffinitedifferenceswhicharetakenfromthemonographofAgarwal(2000).Chapter2providessomeresultsintheoscillationoffirstorderdelaydifferenceequations.Chapter3discussesoscillation,nonoscillationandasymptoticclassificationofnonoscillatorysolutionsofsecondnonlineardifferenceequations.Chapter4investigatestheoscillationandexistenceofnonoscillatorysolutionsofhigherorderneutraldelaydifferenceequations.Chapter5dealswithoscillationfordelaydifferenceequationswithcontinuousvariables.Chapter6concernsoscillationandnonoscillationoffunctionalequations.Thelastchapter,Chapter7studiesoscillationandexistenceofnonoscillatorysolutionsofdelaypartialdifferenceequations.
目录
Preface
Chapter1Preliminaries
1.0Introduction
1.1Notations
1.2Definitions
1.3SomeBasicTheoremsonCalculusofFiniteDifferences
1.4SomeFixedPointTheorems
Chapter2　FirstOrderDelayDifferenceEquations
2.0Introduction
2.1OscillationofFirstOrderDelayDifferenceEquationsinCriticalStates
2.2OscillationofFirstOrderDelayDifferenceEquationswithVariableDelays
2.3SemicyclesoftheOscillatorySolutionsofFirstOrderDelayDifferenceEquations
2.4Notes
Chapter3SecondOrderDelayDifferenceEquations
3.0Introduction
3.1OscillationandNonoscillationofSecondOrderHalf-LinearDifferenceEquations
3.2ClassificationofNonoscillatorySolutionsofSecondOrderNonlinearNeutralDelayDifferenceEquations
3.3ExistenceofNonoscillatorySolutionsofSecondOrderNonlinearNeutralDelayDifferenceEquations
3.4Notes
Chapter4HigherOrderDelayDifferenceEquations
4.0Introduction
4.1OscillationofHigherOrderLinearDifferenceEquations
4.2OscillationofHigherOrderLinearNeutralDelayDifferenceEquations
4.3ComparisonTheoremsforOscillationofHigherOrderNonlinearNeutralDelayDifferenceEquations
4.4ExistenceofNonoscilatorySolutionsofHigherOrderNonlinearNeutralDelayDifferenceEquationss
4.5NonoscillatorySolutionsofHigherOrderNeutralDelayDifferenceEquationswithForcingTerms
4.6ClassificationofNonoscillatorySolutionsofHigherOrderNonlinearNeutralDelayDifferenceEquations
4.7Notes
Chapter5DelayDifferenceEquationswithContinuousVariables
5.0Introduction
5.1TheDistributionofZerosofLinearDifferenceEquationswithContinuousVariables
5.2TheDistributionofZerosofNonlinearDelayDifferenceEquationswithContinuousVariables
5.3OscillationofNonlinearNeutralDifferenceEquationswithContinuousVariables
5.4Notes
Chapter6FunctionalEquations
6.0Introduction
6.1OscillationofFunctionalEquationswithContinuousVariables.
6.2OscillationofNonlinearFunctionalEquations
6.3OscillationofTwo-VariablesFunctionalEquations
6.4Notes
Chapter7PartialDifferenceEquations
7.0Introduction
7.1OscillationofLinearPartialDifferenceEquations
7.2ComparisonTheoremsforOscillationofPartialDifferenceEquations
7.3ExistenceofBoundedandUnboundedNonoscillatorySolutionofPartialDifferenceEquations
7.4Notes
References