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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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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.
EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 78 / Issue 3 / December 2008
- Published online by Cambridge University Press:
- 01 December 2008, pp. 365-382
- Print publication:
- December 2008
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A bounded continuous function
is said to be S-asymptotically ω-periodic if 
. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.
is said to be 
. This paper is devoted to study the existence and qualitative properties of 