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Elsevier

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

Positive Solutions

  • 1 Edición - 1 de octubre de 2015
  • Última edición
  • Autores: Johnny Henderson, Rodica Luca
  • Idioma: Inglés

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings to… Leer más

Descripción

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.

Puntos claves

  • 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

De interès para

Graduate students and research faculty at universities

Índice

  • 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

Reseñas

"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

Detalles del producto

  • Edición: 1
  • Última edición
  • Publicado: 30 de octubre de 2015
  • Idioma: Inglés

Sobre los autores

JH

Johnny Henderson

Afiliaciones y experiencia
Department of Mathematics, Baylor University, Waco, Texas, USA

RL

Rodica Luca

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

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