Existence of positive solutions of second‐order delayed differential system on infinite interval. (6th February 2021)

• Record Type: Journal Article
• Authors: Ding, Ran; Wang, Fanglei; Yang, Nannan; Ru, Yuanfang
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 8(2021)
• Page Start: 7238
• Page End: 7249
• Publication Date: 2021-02-06
• Subjects: differential systems -- fixed point theorem -- positive solutions -- two delays; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7256
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The present paper is focused on the analysis on the existence of positive solutions of a second‐order differential system with two delays x 1 ′ ′ ( t ) − a 1 ( t ) x 1 ( t ) + m 1 ( t ) f 1 ( t, x ( t ), x τ ( t ) ) = 0, t > 0, x 2 ′ ′ ( t ) − a 2 ( t ) x 2 ( t ) + m 2 ( t ) f 2 ( t, x ( t ), x τ ( t ) ) = 0, t > 0, x 1 ( t ) = 0, − τ 1 ≤ t ≤ 0, and lim t → ∞ x 1 ( t ) = 0, x 2 ( t ) = 0, − τ 2 ≤ t ≤ 0, and lim t → ∞ x 2 ( t ) = 0 by using two well‐known fixed point theorems.