Small Solutions and Completeness for Linear Functional Differential Equations

摘要

A class of unbounded operators is presented that in particular contains the generator for functional differential equations. It is possible for this class of operators to state necessary and sufficient conditions in order to have a complete system of eigenfunctions and generalized eigenfunctions. As an illustration of the abstract results, the authors consider both autonomous and periodic functional differential equations. In particular, if the delays are integer multiples of the period, the authors present necessary and sufficient conditions in order to have a complete system of Floquet solutions.