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Stability of asymptotic properties of Hille-yosida operators under perturbations and retarded differential equations
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lahcen ManiarWe give conditions on the strongly continuous semigroup (T 0(t)) t≥0, generated by the part of a Hille-Yosida operator A on X 0 := D(A), and a non-autonomous family of operators (B(t)) t≥0 such that the evolution family (U(t,s)) t≥s≥0,... -
Reliable finite element methods for self-adjoint singular perturbation problems
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: JeanM.-S. Lubuma --- Department of Mathematics and Applied Mathematics, South Africa KailashC. Patidar --- Department of Mathematics and Applied Mathematics, South AfricaIt is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular... -
A note on a conjecture concerning rank one perturbations of singular M-matrices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: B. Anehila --- ROC Mondriaan, The Netherlands A.C.M. Ran --- VU Amsterdam, The NetherlandsA conjecture from [3] concerning the location of eigenvalues of rank one perturbations of singular M-matrices is shown to be false in dimension four and higher, but true for dimension two, as well as for dimension three with an additional... -
Perturbations with nonpositive Lyapunov exponents
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Luis Barreira --- Instituto Superior Técnico, Universidade de Lisboa, Portugal Claudia Valls --- Instituto Superior Técnico, Universidade de Lisboa, PortugalThe notion of uniform hyperbolicity is equivalent to various admissibility properties. For example, one such property is expressed in terms of the existence of bounded solutions for any bounded perturbation of the dynamics. Our main objective is to describe a... -
One-sided Drazin invertibility in Banach algebras and perturbations of B-Fredholm spectra
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Kai Yan --- Fuzhou University, P.R. ChinaThe famous Drazin inverse and generalized Drazin inverse were originally introduced by Drazin in 1958 and Koliha in 1996, respectively. In this paper, the author presents simplified notions of left and right (generalized) Drazin inverses, which are the one-sided versions...