数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (3): 337-345.

• 论文 • 上一篇    下一篇

POSITIVE SOLUTIONS OF HIGHER ORDER SUBLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

缪益华   

  1. Dept. of Appl. Math., Southwestern Jiaotong Univ., Chengdu 610031, China
  • 收稿日期:1990-12-18 出版日期:1992-09-25 发布日期:1992-09-25

POSITIVE SOLUTIONS OF HIGHER ORDER SUBLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Miao Yihua   

  1. Dept. of Appl. Math., Southwestern Jiaotong Univ., Chengdu 610031, China
  • Received:1990-12-18 Online:1992-09-25 Published:1992-09-25

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摘要： In this paper, we discuss higher order sublinear functional differential equation
x(n)(t)+p(t)xv(g(t))=0 t ≥ t0
where n ≥ 2,0 < v < 1,p(t)∈C(R+,R+),g(t)∈C([t0,∞),R+),0 ≤ g(t) ≤ t (t ≥ t0) and
limt→∞g(t)=∞.R+=[0,∞).
Some necessary and sufficient conditions for existence of positive solution of the equation are established.

Abstract: In this paper, we discuss higher order sublinear functional differential equation
x(n)(t)+p(t)xv(g(t))=0 t ≥ t0
where n ≥ 2,0 < v < 1,p(t)∈C(R+,R+),g(t)∈C([t0,∞),R+),0 ≤ g(t) ≤ t (t ≥ t0) and
limt→∞g(t)=∞.R+=[0,∞).
Some necessary and sufficient conditions for existence of positive solution of the equation are established.

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