Agarwal, Ravi P., O'Regan, D. 　著

内容

目次

Preface.- Introduction.- Historical Notes.- Exact Equations.- ElementaryFirst Order Equations.- First Order Linear Equations.- Second Order LinearEquations.- Preliminaries to Existence and Uniqueness of Solutions.- Picard'sMethod of Successive Approximations.- Existence Theorems.- UniquenessTheorems.- Differential Inequalities.- Continuous Dependence on InitialConditions.- Preliminary Results from Algebra and Analysis.- PreliminaryResults from Algebra and Analysis (Contd.).- Existence and Uniqueness ofSolutions of Systems.- Existence and Uniqueness of Solutions of Systems(Contd.).- General Properties of Linear Systems.- Fundamental MatrixSolution.- Systems with Constant Coefficients.- Periodic Linear Systems.-Asymptotic Behavior of Solutions of Linear Systems.- Asymptotic Behavior ofSolutions of Linear Systems (Contd.).- Preliminaries to Stability ofSolutions.- Stability of Quasi--Linear Systems.- Two--Dimensional AutonomousSystems.- Two--Dimensional Autonomous Systems (Contd.).- Limit Cycles andPeriodic Solutions.- Lyapunov's Direct Method for Autonomous Systems.-Lyapunov's Direct Method for Non--Autonomous Systems.- Higher Order Exact andAdjoint Equations.- Oscillatory Equations.- Linear Boundary Value Problems.-Green's Functions.- Degenerate Linear Boundary Value Problems.- MaximumPrinciples.- Sturm--Liouville Problems.- Sturm--Liouville Problems (Contd.).-Eigenfunction Expansions.- Eigenfunction Expansions (Contd.).- NonlinearBoundary Value Problems.- Nonlinear Boundary Value Problems (Contd.).- Topicsfor Further Studies.- References.- Index