A well-posedness result for a class of linear difference equations Original Research Article

In this note, we prove a well-posedness result for a class of linear difference equations in the space of all real sequences {vr}r∈N∪{0} satisfying supr∈N∪{0}r! |vr| < +∞. Such result is obtained as an application of a recent result on the well posedness of the Cauchy problem for ordinary differential equations in the space of all functions View the MathML source (where E is a Banach space) whose derivatives are equibounded on each bounded subset of R.