A New Class of $$(\omega ,c)$$-Periodic Non-instantaneous Impulsive Differential Equations

$ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations

“…By (15), then (16) tends to zero when → 0. Thus K can be approximated to an arbitrary degree of accuracy by a precompact set K .…”

“…Li et al [14] studied (ω, c)periodic solutions of impulsive differential systems with coefficient of matrices. Liu et al [15] studied a new class of (ω, c)-periodic non-instantaneous impulsive differential equations, and establish existence and uniqueness of (ω, c)-periodic solutions for nonlinear impulsive problem via fixed point theorems. Chang et al [9] presented the existence of rotating periodic solutions of second order dissipative dynamical systems.…”

“…Let T : X → X be a linear isomorphism, X is a Banach space and ω > 0, motivated by [2,3,11,14,15], we study the (ω, T)-periodic solutions of the following semilinear impulsive differential equations…”

Non‐instantaneous impulsive fractional integro‐differential equations with proportional fractional derivatives with respect to another function

“…For more recent contributions relevant to non‐instantaneous impulsive fractional differential equations, we refer the reader to previous papers 16–20 and references cited therein.…”

Hartman and Nirenberg type results for systems of delay differential equations under $ (\omega,Q) $-periodic conditions

“…Furthermore, various generalizations such as c-semiperiodic, c-almost periodic functions were considered in [12,13]. Many other extensions to impulsive, discrete or fractional differential equations have been investigated in [5,6], Agaoglou et al [2] studied the existence and uniqueness of (ω, c)-periodic solutions of impulsive evolution equations in complex Banach spaces, Li et al [16] studied (ω, c)-periodic solutions of impulsive differential with matrix coefficients, Liu et al [17], [18] considered noninstantaneous impulsive differential equations establishing existence and uniqueness of (ω, c)-periodic solutions for semilinear problems. When dealing with a system instead of a scalar equation, the (ω, c)-periodic solutions can be regarded as a particular case of the so-called affine-periodic functions; namely, continuous vector functions X ∈ C(R, R n ) such that X(t + ω) = QX(t) for some invertible matrix Q.…”