Abstract
We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as(*)
for where
is the generator of a
-semigroup defined on a Banach space
,
denote fractional difference in Weyl-like sense and
satisfies Lipchitz conditions of global and local type. We introduce the notion of
-resolvent sequence
and we prove that a mild solution of
corresponds to a fixed point of
We show that such mild solution is strong in case of the forcing term belongs to an appropriate weighted Lebesgue space of sequences. Application to a model of population of cells is given.
Notes
No potential conflict of interest was reported by the authors.