Boundary Value Problems for Systems of Differential, Difference and Fractional Equations - 1st Edition - ISBN: 9780128036525, 9780128036792

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

1st Edition

Positive Solutions

Authors: Johnny Henderson Rodica Luca
eBook ISBN: 9780128036792
Paperback ISBN: 9780128036525
Imprint: Elsevier
Published Date: 1st October 2015
Page Count: 322
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Description

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions.

As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.

To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.

Key Features

  • Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions
  • Discusses second order difference equations with multi-point boundary conditions
  • Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Readership

Graduate students and research faculty at universities

Table of Contents

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  • Dedication
  • Preface
  • About the authors
  • Acknowledgments
  • 1: Systems of second-order ordinary differential equations with integral boundary conditions
    • Abstract
    • 1.1 Existence of positive solutions for systems with parameters
    • 1.2 Nonexistence of positive solutions
    • 1.3 Existence and multiplicity of positive solutions for systems without parameters
    • 1.4 Systems with singular nonlinearities
    • 1.5 Remarks on some particular cases
    • 1.6 Boundary conditions with additional positive constants
  • 2: Systems of higher-order ordinary differential equations with multipoint boundary conditions
    • Abstract
    • 2.1 Existence and nonexistence of positive solutions for systems with parameters
    • 2.2 Existence and multiplicity of positive solutions for systems without parameters
    • 2.3 Remarks on a particular case
    • 2.4 Boundary conditions with additional positive constants
    • 2.5 A system of semipositone integral boundary value problems
  • 3: Systems of second-order difference equations with multipoint boundary conditions
    • Abstract
    • 3.1 Existence and nonexistence of positive solutions for systems with parameters
    • 3.2 Existence and multiplicity of positive solutions for systems without parameters
    • 3.3 Remarks on some particular cases
    • 3.4 Boundary conditions with additional positive constants
  • 4: Systems of Riemann–Liouville fractional differential equations with uncoupled integral boundary conditions
    • Abstract
    • 4.1 Existence and nonexistence of positive solutions for systems with parameters and uncoupled boundary conditions
    • 4.2 Existence and multiplicity of positive solutions for systems without parameters and uncoupled boundary conditions
    • 4.3 Uncoupled boundary conditions with additional positive constants
    • 4.4 A system of semipositone fractional boundary value problems
  • 5: Systems of Riemann–Liouville fractional differential equations with coupled integral boundary conditions
    • Abstract
    • 5.1 Existence of positive solutions for systems with parameters and coupled boundary conditions
    • 5.2 Existence and multiplicity of positive solutions for systems without parameters and coupled boundary conditions
    • 5.3 Coupled boundary conditions with additional positive constants
    • 5.4 A system of semipositone coupled fractional boundary value problems
  • Bibliography
  • Index

Details

No. of pages:
322
Language:
English
Copyright:
© Elsevier 2016
Published:
Imprint:
Elsevier
eBook ISBN:
9780128036792
Paperback ISBN:
9780128036525

About the Author

Johnny Henderson

Affiliations and Expertise

Department of Mathematics, Baylor University, Waco, Texas, USA

Rodica Luca

Affiliations and Expertise

Department of Mathematics, “Gheorghe Asachi” Technical University of Iasi, Romania

Reviews

"This well-written book is a collection of recent works by the authors who are pioneering researchers in the community of differential and difference equations...This text is a great resource for graduate students and scholars to learn classic methods and latest development in this field." --Zentralblatt MATH

"The monograph contains an extensive bibliography and is suitable, as a reference book, for many researchers specializing in positive solutions and graduate students interested in this field." --Mathematical Reviews