Abstract
By using a multiple fixed point theorem (Avery-Peterson fixed point theorem) for cones, some criteria are established for the existence of three positive periodic solutions for a class of higher-dimensional functional differential equations with impulses on time scales of the following form: , , , where is a nonsingular matrix with continuous real-valued functions as its elements. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.
Highlights
Impulsive delay differential equations may express several real-world simulation processes which depend on their prehistory and are subject to short-time disturbances
Based on a fixed-point theorem in cones, Li et al 5 investigated the periodicity of the following scalar system: yt −atytgt, y t − τ t, t / tj, j ∈ Z, 1.1 y tj y t−j Ij y tj, Advances in Difference Equations where a ∈ C R, 0, ∞, τ ∈ C R, R, g ∈ C R× 0, ∞, 0, ∞, Ij ∈ C 0, ∞, 0, ∞, j ∈ Z, and a t, τ t are ω-periodic functions and g t, y is ω-periodic with respect to its first argument
Our main aim of this paper is to use a multiple fixed point theorem Avery-Peterson fixed point theorem for cones to establish the existence of three positive periodic solutions of 1.3
Summary
Impulsive delay differential equations may express several real-world simulation processes which depend on their prehistory and are subject to short-time disturbances. In this paper, we consider the following system: xΔ tAtxtft, xt , t / tj , j ∈ Z, t ∈ T, 1.3 x tj x t−j Ij x tj , where T is an ω-periodic time scale, A t aij t n×n t ∈ T is a nonsingular matrix with continuous real-valued functions as its elements, and AtωAt ; f f1, f2, . Our main aim of this paper is to use a multiple fixed point theorem Avery-Peterson fixed point theorem for cones to establish the existence of three positive periodic solutions of 1.3.
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