Abstract
In this paper, we study the existence of affine-periodic solutions of nonlinear impulsive differential equations. The affine-periodic solutions have the form x(t+T)=Qx(t) with some nonsingular matrix Q. We give a theorem on the existence of the affine-periodic solutions, respectively, depending on wether operatorname{det}(I-Q) (I= identity matrix) is equal to 0 or not.
Highlights
The periodicity is a very important property in the study of the impulsive differential equations [1, 2]
Where f : R1 × Rn → Rn is continuous, and for some Q ∈ GLn(R), satisfies the following affine symmetry: f (t + T, x) = Qf t, Q–1x. We call it a (Q, T)-affine-periodic system. For this (Q, T)-affine-periodic system, we are concerned with the existence of (Q, T)-affine-periodic solutions x(t) with x(t + T) = Qx(t), ∀t
Via the topological degree theory, we prove the existence of affine-periodic solutions for nonlinear impulsive system when det(I – Q) = 0 in Sect
Summary
The periodicity is a very important property in the study of the impulsive differential equations [1, 2]. We call it a (Q, T)-affine-periodic system. The aim of this paper is to touch such a topic for affine-periodic solutions of nonlinear impulsive differential equations. We first change the affine-periodic solutions problem to the boundary value problem in Sect.
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