Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces

Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations

“…Recently, the existence and uniqueness of pseudo almost automorphic mild solutions to differential equations in Banach spaces has attracted many researchers (see, e.g., [1][2][3][4][5][6][7][8][9]). In particular, in [2] Xiao, Liang and Zhang proved that the space (PAA(X), · ∞ ) is a Banach space and established sufficient conditions for the existence and uniqueness of pseudo almost automorphic mild solutions to semilinear differential equations in Banach spaces, in [3] Xiao, Zhu and Liang introduced a new concept of bi-almost automorphic function and obtained new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations, thus pushed the door open to study pseudo almost automorphic mild solutions to nonautonomous evolution equations.…”

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

“…Such a concept, since its introduction in the literature, has recently generated several developments; see, for example, [8][9][10][11][12] . The question which consists of the existence of pseudo-almost automorphic solutions to abstract partial evolution equations has been made; see for instance 10,11,13 . However, the use of Krasnoselskii fixed point principle to establish the existence of pseudo-almost automorphic solutions to nonautonomous partial evolution equations in the form 1.2 is an original untreated problem, which is the main motivation of the paper.…”

Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

“…[8] introduced the concept of µ-pseudo almost periodicity, is a natural generalization of the classical concept of weighted pseudo almost periodicity in the sense of Diagana [18,20]. More recently, [9] introduced the concept of µ-pseudo almost automorphy, is a natural generalization of the classical concept of weighted pseudo almost automorphic in the sense of Diagana [21,22,24]. In recent paper [32], authors gave a results on the existence and uniqueness of pseudo almost periodic solution for equations (1.1), where the impute function is S p pseudo almost periodic.…”