Periodic solutions of a class of integrodifferential impulsive periodic systems with time-varying generating operators on Banach space

A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces

“…Recently, the impulsive evolution equations and its optimal control problems on infinite dimensional Banach spaces have been investigated by many authors including Ahmed, Ntouyas, Liu, and us (see for instance [1][2][3][4][5][6]20,[30][31][32][33] and references therein). Particularly, by constructing impulsive periodic evolution operators and generalized Gronwall inequalities, we studied the integrodifferential impulsive periodic evolution equations on infinite dimensional spaces (see [26][27][28][29]). …”

$(ω,ρ)$-Periodic solutions of abstract integro-differential impulsive equations on Banach space

“…The existence of piecewise continuous mild solutions and optimal control of integro-differential systems is presented in [41]. In [36]- [37], the integro-differential impulsive periodic systems on infinite-dimensional spaces are discussed. To our best knowledge, the existence and uniqueness of (ω, c)-periodic solutions for integro-differential systems (c ∈ C, c = 0) have not been extensively studied.…”

Existence and uniqueness of (ω,c)-periodic solutions of semilinear evolution equations

“…Obviously, (ω, c)-periodic functions reduce to the standard ω-periodic functions when c = 1, and to ω-antiperiodic ones when c = −1. These last particular cases are already intensively studied (see [2,3,7,9,10,12]).…”