Graef John R's Books

Implicit Fractional Differential and Integral Equations

Existence and Stability

By: Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson

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Implicit Fractional Differential and Integral Equations

Existence and Stability

By: Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. 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. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

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Page Count

362

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110553813

ISBN 13

9783110553819

Multiple Solutions Of Boundary Value Problems: A Variational Approach

By: John R Graef,Lingju Kong

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Multiple Solutions Of Boundary Value Problems: A Variational Approach

By: John R Graef,Lingju Kong

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.

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290

Publisher

World Scientific

Published Date

ISBN 10

9814696560

ISBN 13

9789814696562

The Nonlinear Limit-Point/Limit-Circle Problem

By: Miroslav Bartusek,Zuzana Dosla,John R. Graef

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The Nonlinear Limit-Point/Limit-Circle Problem

By: Miroslav Bartusek,Zuzana Dosla,John R. Graef

This self-contained monograph traces the evolution of the limit–point/limit–circle problem from its 1910 inception, in a paper by Hermann Weyl, to its modern-day extensions to the asymptotic analysis of nonlinear differential equations. The authors distill the classical theorems in the linear case and carefully map the progress from linear to nonlinear limit–point results. The relationship between the limit–point/limit–circle properties and the boundedness, oscillation, and convergence of solutions is explored, and in the final chapter, the connection between limit–point/limit–circle problems and spectral theory is examined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields.

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Page Count

168

Publisher

Springer Science & Business Media

Published Date

ISBN 10

081768218X

ISBN 13

9780817682187

Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics

By: Seshadev Padhi,John R. Graef,P. D. N. Srinivasu

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Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics

By: Seshadev Padhi,John R. Graef,P. D. N. Srinivasu

This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.

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Page Count

155

Publisher

Springer

Published Date

ISBN 10

8132218957

ISBN 13

9788132218951

Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations

By: John R Graef,Johnny L Henderson,Lingju Kong,Sherry Xueyan Liu

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Ordinary Differential Equations And Boundary Value Problems - Volume I: Advanced Ordinary Differential Equations

By: John R Graef,Johnny L Henderson,Lingju Kong,Sherry Xueyan Liu

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.

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177

Publisher

World Scientific

Published Date

ISBN 10

9813236477

ISBN 13

9789813236479

Oscillation and Dynamics in Delay Equations

Proceedings of an AMS Special Session Held January 16-19, 1991

By: John R. Graef,Jack K. Hale,American Mathematical Society. Meeting

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Oscillation and Dynamics in Delay Equations

Proceedings of an AMS Special Session Held January 16-19, 1991

By: John R. Graef,Jack K. Hale,American Mathematical Society. Meeting

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 modelling, 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.

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274

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821851403

ISBN 13

9780821851401

The Strong Nonlinear Limit-point/limit-circle Problem

By: John R Graef,Miroslav Bartusek

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The Strong Nonlinear Limit-point/limit-circle Problem

By: John R Graef,Miroslav Bartusek

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.

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Page Count

325

Publisher

World Scientific

Published Date

ISBN 10

9813226390

ISBN 13

9789813226395

Impulsive Differential Inclusions

A Fixed Point Approach

By: John R. Graef,Johnny Henderson,Abdelghani Ouahab

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Impulsive Differential Inclusions

A Fixed Point Approach

By: John R. Graef,Johnny Henderson,Abdelghani Ouahab

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.

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Page Count

412

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110295318

ISBN 13

9783110295313

Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems

By: John R Graef,Johnny L Henderson,Lingju Kong,Sherry Xueyan Liu

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Ordinary Differential Equations And Boundary Value Problems - Volume Ii: Boundary Value Problems

By: John R Graef,Johnny L Henderson,Lingju Kong,Sherry Xueyan Liu

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.While this Volume II complements , it can be used as a stand-alone work.

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343

Publisher

World Scientific

Published Date

ISBN 10

9813274042

ISBN 13

9789813274044

Topological Methods for Differential Equations and Inclusions

By: John R. Graef,Johnny Henderson,Abdelghani Ouahab

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Topological Methods for Differential Equations and Inclusions

By: John R. Graef,Johnny Henderson,Abdelghani Ouahab

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.

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Page Count

425

Publisher

CRC Press

Published Date

ISBN 10

0429822618

ISBN 13

9780429822612

Practicing Post-Liberal Peacebuilding

Legal Empowerment and Emergent Hybridity in Liberia

By: Julian Graef

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Practicing Post-Liberal Peacebuilding

Legal Empowerment and Emergent Hybridity in Liberia

By: Julian Graef

Practicing Post-Liberal Peacebuilding engages with one of the central debates in Peace and Conflict Studies and International Relations. The book's innovation lies in the introduction and application of 'practice theory' to develop a critical methodology for mapping the everyday practices of post-liberal hybridity in Liberia.

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