Green's functions in the theory of ordinary differential equations [electronic resource] /
Cabada, Alberto.author.
This book provides a complete and exhaustive study of the Green's functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
Description based upon print version of record.
Includes bibliographical references and index.
1. Green's Functions in the Theory of Ordinary Differential Equations -- Appendix A. A Green's Function Mathematica Package -- Appendix B. Expressions of Some Particular Green's Functions.
This book provides a complete and exhaustive study of the Green's functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.
Differential equations.
Functions of complex variables.
Operator theory.
Ordinary Differential Equations.
Several Complex Variables and Analytic Spaces.
Operator Theory.