RT journal article
T1 Lebesgue regularity for differential difference equations with fractional damping
A1 Leal, C.
A1 Lizama, Carlos
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Delay
K1 Differential difference equations
K1 Fractional differences
K1 Lebesgue maximal regularity
AB We provide necessary and sufficient conditions for the existence and uniqueness of solutions   belonging to the vector-valued space of sequences $ \ell_p(\Z,X)$ for equations that can be modeled in the form$$\Delta^{\alpha}u(n)+\lambda \Delta^{\beta}u(n)=Au(n) + G(u)(n) + f(n),\, n \in \Z, \, \alpha, \beta >0,\, \lambda \geq  0,$$where $X$ is a Banach space,  $f\in\ell_p(\Z,X),$  $A$ is a closed linear operator with domain $D(A)$ defined on $X$ and $G$ is a nonlinear function. The  operator  $\Delta^{\gamma}$  denotes the fractional difference operator of order $\gamma> 0$ in the sense of Gr\"unwald-Letnikov. Our class of models includes the discrete time Klein-Gordon, telegraph and Basset equations, among other differential difference equations of interest. We prove a simple criterion that shows the existence of solutions  assuming that $f$ is smalland that  $G$ is a nonlinear term.
PB Wiley
SN 1099-1476
YR 2018
FD 2018
LK http://hdl.handle.net/10498/35418
UL http://hdl.handle.net/10498/35418
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026