Pseudo almost periodic solutions for a class of first order differential iterative equations

Abstract

a b s t r a c tThis paper is concerned with a class of first order differential iterative equations. Under proper conditions, we employ a novel argument to establish a criterion on the existence of pseudo almost periodic solutions. The obtained result complements with some existing ones.

New results on positive almost periodic solutions for first-order neutral differential equations

“…x(t) - Remark 3.1 In equation (3.1), τ 1 (t) = 1 + sin 2 t and τ 2 (t) = 1 + sin 2 √ 3t are two different time-varying functions, and Q(t) = 1 + 2 sin 400t fails to satisfy (1.3). One can see that all the results obtained in [1][2][3][4][5][6][7][8][9][10][11][12]15] are invalid for (3.1). Note that the space of almost periodic functions contains the space of periodic functions.…”

“…It is well known that almost periodically variable coefficients and delays in differential equations of population and ecology problems are much more realistic in the real world. Therefore, in recent years, there has been increasing interest in the existence and stability of almost periodic type solutions for firstorder functional differential equations in population models [8][9][10][11][12]. However, to the best of our knowledge, there are few papers published on positive almost periodic solutions of (1.1) and (1.2).…”

Pseudo almost periodic solutions of an iterative equation with variable coefficients

“…It is obviously that iterative functional differential equations are special type state-dependent delay differential equations. In [9], Liu pointed that the properties of the almost periodic functions do not always hold in the set of pseudo almost periodic functions and given an example: when x.t / is a pseudo almost periodic function, x.x.t // may not be a pseudo almost periodic function. To the best of our knowledge, there are few results about pseudo almost periodic solutions for iterative functional differential equations except [9] and [16].…”

“…From [9], it is easy to see that B S .M; L/, S 2 fPAP; AP; PAP 0 ; C g are closed convex and bounded subsets of BC.R; R/ and C.R; R/, respectively. Furthermore, by the Arzelá-Ascoli theorem, the subset B C .M; L/ is compact in C.R; R/.…”

Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs

“…Stability, periodicity and almost periodicity are important dynamic characteristics of the systems. Therefore, these behaviors of neural network systems and ecosystems have been extensively studied (see [12][13][14][15][16][17][18][19][20][21][22][23][24]). In addition, we know that weighted pseudo-almost periodicity is an extension of pseudoalmost periodicity and pseudo-almost periodicity.…”