On differential operators with Bohr-Neugebauer type property

On Second-Order Differential Operators With Bohr-Neugebauer Type Property

“…As shown in Rao [4], (« * p n )(t) is bounded on /for all n>\ and (g * p n )(t) is almost periodic from JtoX for all n> 1.…”

“…So u{i) is almost periodic from / to X, which completes the proof of the theorem. 4. Notes, (i) For p=l, our Theorem remains valid for any ^-bounded uniformly continuous solution of the equation (13).…”

“…From this representation, we can show that u'(t) is uniformly continuous on / (see Rao [4]). Now consider a sequence {/>"(*)} °°OE of non-negative continuous functions on / such that (3.2) p n (0 = 0 for \t\>.n-\\ n Pn (t) dt = 1.…”

Almost Periodicity of All $L^2$-bounded Solutions of a Functional Heat Equation

“…There have been much research activity for the qualitative behavior of partial differential equations with or without delays, see, e.g., the references [1-3, 6, 8, 9, 13, 14]. It is worth mentioning that the authors in [4,7,11,12,15] studied the Bohr-Neugebauer property for some special abstract differential equations. A differential equation is said to has Bohr-Neugebauer property if its any bounded solution is almost periodic.…”

Behavior of bounded solutions for some almost periodic neutral partial functional differential equations

“…For every , the history function u t ∈ C is defined by The existence of almost periodic solutions for differential equations has been extensively studied in the last 40 years. We specially mention the works of . In the literature, several books are devoted to cover this topic.…”