Edgardo Alvarez, Carlos Lizama
Abstract:
We study weighted pseudo almost automorphic solutions for the nonlinear
fractional difference equation
for
,
where A is the generator of an
-resolvent
sequence
in
.
We prove the existence and uniqueness of a weighted pseudo almost automorphic
solution assuming that f(.,.) is weighted almost automorphic
in the first variable and satisfies a Lipschitz (local and global)
type condition in the second variable. An analogous result is also proved
for
-asymptotically
-periodic solutions.
Submitted July 5, 2016. Published October 7, 2016.
Math Subject Classifications: 32N05, 65Q10, 47B39.
Key Words: Weyl-like fractional difference; fractional difference equation;
weighted pseudo almost automorphic sequence;
alpha-resolvent sequences of operators
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Edgardo Alvarez Universidad del Norte Departamento de Matemáticas y Estadística Barranquilla, Colombia email: ealvareze@uninorte.edu.co | |
Carlos Lizama Universidad de Santiago de Chile Facultad de Ciencia Departamento de Matemática y Ciencia de la Computacióon Las Sophoras 173, Estación Central Santiago, Chile email: carlos.lizama@usach.cl |
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