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Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in Lp Spaces
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 62 / Issue 1 / 01 February 2010
- Published online by Cambridge University Press:
- 20 November 2018, pp. 74-93
- Print publication:
- 01 February 2010
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- Article
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We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations
$\left( \text{NFDE} \right)$ in 
${{L}^{p}}$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the 
$\text{NFDE}$ as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.
