Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces

摘要

We present the explicit formulas for the projectors on the generalizedeigenspaces associated with some eigenvalues for linear neutral functionaldifferential equations (NFDE) in $L^{p}$ spaces by using integratedsemigroup theory. The analysis is based on the main resultestablished elsewhere by the authors and results by Magal and Ruanon non-densely defined Cauchy problem.We formulate the NFDE as a non-densely defined Cauchy problem and obtainsome spectral properties from which we then derive explicit formulas forthe projectors on the generalized eigenspaces associated with someeigenvalues. Such explicit formulas are important in studying bifurcationsin some semi-linear problems.