Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, etc. The questions of existence and stability of solutions for different classes of initial values problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems and relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Impulsive Differential Inclusions

John R Graef

Walter De Gruyter Gmbh & Co Kg

The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated.

STRONG NONLINEAR LIMIT-POINT/LIMIT-CIRCLE PROBLEM, THE (Trends in Abstract and Applied Analysis)

Science & Math

Miroslav Bartusek

Mathematics

World Scientific Publishing Co Pte Ltd

Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations (Trends in Abstract and Applied Analysis)

The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book. 
 The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well. 
 Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems. 
 Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs. 
 Readership: Graduate students and researchers interested in ordinary differential equations.

ORDINARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS - VOLUME I: ADVANCED ORDINARY DIFFERENTIAL EQUATIONS (Trends in Abstract and Applied Analysis)

Johnny Henderson

Lingju Kong

Xueyan Sherry Liu

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems (Trends in Abstract and Applied Analysis)

The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.
A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.
The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.

ORDINARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS - VOLUME II: BOUNDARY VALUE PROBLEMS (Trends in Abstract and Applied Analysis)

World Scientific Publishing Co.

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Books by John R Graef