二阶脉冲微分方程m点边值问题的正解

Positive solutions to m-point boundary value problems of second order impulsive differential equations

利用Leggett-Williams不动点定理,研究一类二阶脉冲微分方程非局部(m点)边值问题正解的存在性。在某些条件下,得到了它至少存在3个正解u1,u2,u3,使得‖u1‖<d,a<α(u2)且‖u3‖≥d,α(u3)≤a。

By using the Leggett-williams fixed point theorem, this paper studies the existence of positive solutions to m-point boundary value problems of the second order impulsive differential equations. In some conditions, it shows that the above problem has at least three positive solutions u1 ,u2 and so that ｜｜ U1 ｜｜ 〈d,a〈a（u2） and ｜｜ u3 ｜｜ ≥d, a（u3） ≤a.