Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with -weighted pseudo-almost periodic coefficients

Review and Study of Some Doubly-Weighted Pseudo-almost Periodic Solutions of Some Partial Evolution Equations

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] of the most attractive topics in qualitative theory of differential equations due to possible applications. Some contributions on weighted pseudo-almost periodic functions, their extensions, and their applications to differential equations have recently been made, among them are for instance [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein. However, the problem which consists of the existence of doubly-weighted pseudo-almost periodic(mild) solutions to evolution equations in the form (1.1) is quite new and untreated and thus constitutes one of the main motivations of the theme.…”

“…Further, it will be shown that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. In [1], it is proved that for µ,ν ∈ U ∞ and f : R → X an almost periodic function such that…”

“…In [1], results on the existence and uniqueness are provided for doubly-weighted pseudoalmost periodic solution for equations u…”

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

“…N'Guérékata et al [8] presented stepanov-like almost automorphic functions and discussed its application to monotone differential equations. Then, in [9], Diagana introduced the concept of Stepanov-like weighted pseudo almost periodicity and applied the concept to study the existence and uniqueness of weighted pseudo almost periodic solutions to (1.1). In recent years, the existence of almost periodic, pseudo almost periodic, weighted pseudo almost periodic and S p -weighted pseudo almost periodic solutions of various differential equations have been considerably investigated (cf.…”

“…Motivated by the works [9,21,[24][25][26], we present here a new composition theorem for Stepanov-like weighted pseudo almost periodic functions. It is different from the existing ones which are based on Lipschitz conditions.…”