Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January, 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modeling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.

Oscillation and Dynamics in Delay Equations: Proceedings of an Ams Special Session Held January 16-19, 1991 (Contemporary Mathematics)

Science & Math

Graef, John R.

Mathematics

Amer Mathematical Society

<p>Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis. </p>

Topological Methods for Differential Equations and Inclusions (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Henderson, Johnny

Ouahab, Abdelghani

CRC-Press

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models.  During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Impulsive Differential Inclusions: A Fixed Point Approach (De Gruyter Series in Nonlinear Analysis and Applications, 20)

Walter de Gruyter

This book deals with existence and stability issues for solutions to initial and boundary value problems for functional differential and integral equations and inclusions with Caputo's fractional derivative and Hadamard's fractional integral. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus.

Implicit Fractional Differential and Integral Equations: Existence and Stability (De Gruyter Series in Nonlinear Analysis and Applications, 26)

Abbas, Saïd

Benchohra, Mouffak

de Gruyter

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

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

Kong, Lingju

Liu, Xueyan Sherry

WSPC

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

<p>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.</p>

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

Variational methods and their generalizations have been verified to be useful tools in proving the existence of solutions to a variety of boundary value problems for ordinary, impulsive, and partial differential equations as well as for difference equations. In this monograph, we look at how variational methods can be used in all these settings. In our first chapter, we gather the basic notions and fundamental theorems that will be applied in the remainder of this monograph. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with the Sturm-Liouville problems, multi-point boundary value problems, problems with impulses, partial differential equations, and difference equations. An extensive bibliography is also included.

MULTIPLE SOLUTIONS OF BOUNDARY VALUE PROBLEMS: A VARIATIONAL APPROACH (Trends in Abstract and Applied Analysis)

World Scientific Publishing Company

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