The problems of development of constructive methods for the analysis oflinear and weakly nonlinear boundary-value problems for a broad class offunctional differential equations traditionally occupy one of thecentral places in the qualitative theory of differential equations.
The authors of this monograph suggest some methods for the constructionof the generalized inverse (or pseudo-inverse) operators for theoriginal linear Fredholm operators in Banach (or Hilbert) spaces forboundary-value problems regarded as operator systems in abstract spaces.They also study basic properties of the generalized Green's operator.
In the first three chapters some results from the theory of generalizedinversion of bounded linear operators in abstract spaces are given,which are then used for the investigation of boundary-value problems forsystems of functional differential equations. Subsequent chapters dealwith a unified procedure for the investigation of Fredholmboundary-value problems for operator equations; analysis ofboundary-value problems for standard operator systems; and existence ofsolutions of linear and nonlinear differential and difference systemsbounded on the entire axis.
This book will be of value and interest to anyone working in the fieldsof differential equations and nonlinear oscillations.
2004; xiv+318 pages
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