Weighted pseudo-almost periodic solutions to some differential equations

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

“…(H5) The space W P AP (X) is translation invariant, that is, the weighted function ρ ∈ U ∞ and satisfies: Remark 3.1. Note that condition (H5) was introduced by Diagana in [5][6][7].…”

“…It is a natural generalization of the classical almost periodicity in the sense of Bochner. Recently, Agarwal and Diagana [4], and Diagana [5][6][7] introduced the concept of weighted pseudo almost periodic functions, which generalizes the one of pseudo almost periodicity. N'Guérékata et al [8] presented stepanov-like almost automorphic functions and discussed its application to monotone differential equations.…”

Translation invariance and related properties of μ-pseudo almost automorphic (periodic) functions with application

“…Then these concepts are generalized in various ways, say, pseudo almost periodicity (Zhang [1][2][3]), weighted pseudo almost periodicity (Diagana [4,5]), pseudo almost automorphy (Liang, Xiao and Zhang [6,7]), weighted pseudo almost automorphy (Blot et al [8]), etc. These concepts have been widely used in the investigation of ordinary differential equations, partial differential equations, functional differential equations and fractional differential equations.…”

Weighted Pseudo-Almost Periodic Solutions for Some Abstract Differential Equations With Uniform Continuity

“…Recently, Diagana [8,10] introduced a new class of functions called weighted pseudo-almost periodic functions, which are a natural generalization of the classical pseudo-almost periodic functions, and discussed the properties of this new class of functions, including a composition result. As applications, some existence and uniqueness theorems for weighted pseudo-almost periodic solutions for abstract differential equations were obtained.…”

“…As applications, some existence and uniqueness theorems for weighted pseudo-almost periodic solutions for abstract differential equations were obtained. We notice that a Lipschitz condition is needed in the composition theorem and its applications in abstract differential equations (see [10,Theorems 3.7,4.2]). So it is interesting and worthwhile to consider the same problem [2] Weighted pseudo-almost periodic solutions 425 under a uniform continuity condition instead of the Lipschitz condition.…”