Green’s Functions in the Theory of Ordinary Differential Equations

1. Front Matter

   Pages i-xiv

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2. Green’s Functions in the Theory of Ordinary Differential Equations

   • Alberto Cabada

   Pages 1-139

3. Back Matter

   Pages 141-168

   PDF

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.

• Boundary Value Problems
• Comparison Results
• Green's Function
• Lower and Upper Solutions
• Monotone Iterative Techniques
• ordinary differential equations

From the book reviews:

“A resource for researchers and graduate students studying boundary value problems for functional differential equations. … the author produces a coherent, useful and quite elegant presentation of the construction of Green’s functions, accompanied by a specific set of applications related to primarily maximum and anti-maximum type principles, comparison theory and methods of upper and lower solutions. … provides a readable and interesting account that will be useful to researchers who want to understand constructions of such operators.” (P. W. Eloe, Mathematical Reviews, July, 2014)

• Department of Mathematical Analysis, University of Santiago de Compostela, Galicia, Spain

  Alberto Cabada

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