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1
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Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces

100%
Keyantuo V., Lizama C.
Studia Mathematica
|
2005
|
tom 168
|
nr 1
25-50
EN
We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.
2
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Periodic solutions of degenerate differential equations in vector-valued function spaces

100%
Lizama C., Ponce R.
Studia Mathematica
|
2011
|
tom 202
|
nr 1
49-63
EN
Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.
3
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Maximal regularity of delay equations in Banach spaces

100%
Lizama C., Poblete V.
Studia Mathematica
|
2006
|
tom 175
|
nr 1
91-102
EN
We characterize existence and uniqueness of solutions for an inhomogeneous abstract delay equation in Hölder spaces. The main tool is the theory of operator-valued Fourier multipliers.
4
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Linear dynamics of semigroups generated by differential operators

81%
Alberto Conejero J., Lizama C., Murillo-Arcila M., Peris A.
Open Mathematics
|
2017
|
tom 15
|
nr 1
745-767
EN
During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss basic properties of the dynamics of C0-semigroups. We will also study in detail the dynamics of the translation C0-semigroup on weighted spaces of integrable functions and of continuous functions vanishing at infinity. Using the comparison lemma, these results can be transferred to the solution C0-semigroups of some partial differential equations. Additionally, we will also visit the chaos for infinite systems of ordinary differential equations, that can be of interest for representing birth-and-death process or car-following traffic models.
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