Premium
Existence of positive solutions of second‐order delayed differential system on infinite interval
Author(s) -
Ding Ran,
Wang Fanglei,
Yang Nannan,
Ru Yuanfang
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7256
Subject(s) - mathematics , interval (graph theory) , order (exchange) , fixed point theorem , differential equation , mathematical analysis , second order equation , fixed point , combinatorics , finance , economics
The present paper is focused on the analysis on the existence of positive solutions of a second‐order differential system with two delaysx 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 , andlim t → ∞x 1 ( t ) = 0 ,x 2 ( t ) = 0 , − τ 2≤ t ≤ 0 , andlim t → ∞x 2 ( t ) = 0by using two well‐known fixed point theorems.