Asymptotic behavior of solutions to abstract functional differential equations

In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form u ˙ ( t ) = A u ( t ) + [ B u ] ( t ) + f ( t ) , t ∈ R . An example is given to illustrate our results.