Asymptotic behavior of evolution systems in arbitrary Banach spaces using general almost periodic splittings - Kreulich, Josef (Advances in nonlinear analysis, 2019)
We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations, and their whole line analogues, , , with a family of ω-dissipative operators in a general Banach space . According to the classical DeLeeuw–Glicksberg theory, functions of various generalized almost periodic types uniquely decompose in a “dominating” and a “damping” part. The second main object of the study – in the above context – is to determine the corresponding “dominating” part of the operators , and the corresponding “dominating” differential equation,