Almost automorphic solutions of certain abstract differential equations

Existence of positive almost automorphic solutions to nonlinear delay integral equations

“…Veech studied almost automorphic functions on groups in [18]. Extension of the concept to vector-valued functions was realized by Zaki (see [19]), paving the road to many applications in ordinary as well as abstract differential equations. Now, almost automorphic functions and their applications have been of great interest for many mathematicians since almost automorphy sometimes is closer to reality than periodicity and almost periodicity (see, e.g., [11]).…”

On Favard's theorems

“…Veech [48,49] and others ( [3,14,23,25,[34][35][36]45,52] and the references therein). The almost automorphic solutions of differential equations were investigated in a series of recent works, see [5,12,15,21,35,37,45,55] and the references therein. Almost automorphic dynamics is known to be fundamental in almost periodically forced differential equations.…”

Square-mean almost automorphic solutions to some stochastic evolution equations I: Autonomous case

“…For more details on almost automorphy and stochastic differential equations, the readers are referred to [1,[6][7][8][9][10]16,17] and the references therein.…”