Affine-periodic solutions by averaging methods

The existence of affine-periodic solutions for nonlinear impulsive differential equations

“…Recently, these conceptions and existence results of the solutions have been introduced and proved by Li and his coauthors; see [5] for Levinson's problem, [6] for Lyapunov function type theorems, [7] for averaging methods of affine-periodic solutions, and [8] for some dissipative dynamical systems. The aim of this paper is to touch such a topic for affine-periodic solutions of nonlinear impulsive differential equations.…”

“…Then we give the following existence theorem for (Q,T)-affine-periodic solutions by using the topological degree theory [6,7,[9][10][11]. …”

Affine-periodic solutions by asymptotic and homotopy equivalence

“…Recently, the concept of affine periodicity, including the spiral symmetry was introduced. Some problems and methods concerning affine-periodic solutions, such as Levinson's problem, Lyapunov function type theorems, the dissipative second order rotating periodic systems, LaSalle type theorems, Hamiltonian systems and the averaging method of higher order perturbed systems were given; see [8,16,18,19,23,24,28].…”

Affine Periodic Solutions of Stochastic Differential Equations

“…The affine periodic systems contain several special cases, such as periodic systems (Q = I l ), anti-periodic systems (Q = −I l ) and rotation periodic systems (Q ∈ O(l)), which are discussed in many literatures like [44,11,29,2]. For general affine matrix Q, Y. Li et al [4,25,32,42,43,45] obtained the existence of affine-periodic solutions for several kinds of deterministic affine-periodic systems.…”