location:  Publications → journals
Search results

Search: MSC category 34K05 ( General theory )

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2009 (vol 62 pp. 74)

Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre
 Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) 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 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. Keywords:neutral functional differential equations, semi-linear problem, integrated semigroup, spectrum, projectorsCategories:34K05, 35K57, 47A56, 47H20

2. CJM 2007 (vol 59 pp. 127)

Lamzouri, Youness
 Smooth Values of the Iterates of the Euler Phi-Function Let $\phi(n)$ be the Euler phi-function, define $\phi_0(n) = n$ and $\phi_{k+1}(n)=\phi(\phi_{k}(n))$ for all $k\geq 0$. We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\phi_k(n)$ is $y$-smooth, conditionally on a weak form of the Elliott--Halberstam conjecture. Categories:11N37, 11B37, 34K05, 45J05