Existence of positive periodic solutions for two types of second-order nonlinear neutral differential equations with variable delay

Abstract

In this article we study the existence of positive periodic solutions for two types of second-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here generalize the work of Cheung, Ren and Han [7].Subjclass : [2000] Primary 34K13, 34A34; Secondary 34K30, 34L30.

Existence of positive periodic solution of second-order neutral differential equations

“…By Lemma 2.7, there is an x ∈ Ω such that S 1 x + S 2 x = x. It is easy to see that x(t) is a positive ω -periodic solution of (2). This completes the proof.…”

Positive periodic solutions for second-order neutral differential equations with time-dependent deviating arguments

“…which is a particular case of equation (1). By applications of a fixed point theorem in cones, some sufficient conditions of existence, multiplicity and nonexistence of positive periodic solutions were established with c ∈ (−1, 0).…”

“…where |c| < 1. Differing from equation (1), the deviating argument of equation 3is the same as the time delay term. By means of Krasnoselskii's fixed point theorem, they obtained sufficient conditions for the existence of periodic solutions to equation (3).…”

Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem

“…Existence, uniqueness, stability and positivity of solutions of functional differential equations are of great interest in mathematics and its applications to the modeling of various practical problems (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) and references therein. Positivity is one of the most common and most important characteristics of mathematical models.…”

“…In the last 50 years, delay models are becoming more common, appearing in many branches of biological, economical and physical modelling (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). This is due to their advantage of combining a simple, intuitive derivation with a wide variety of possible behavior regimes and to the fact that such models operate on an infinite dimensional space consisting of continuous functions that accommodate high dimensional dynamics (see [10][11][12]).…”