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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.
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)
"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)