关于Fr■chet空间中扰动的微分方程一类两点边值问题的正解

POSITIVE SOLUTIONS OF A CLASS OF TWO POINTBOUNDARY VALUE PROBLEM OF PERTURBATIVE DIFFERENTIAL EQUATION IN FRECHET SPACES

设Ｅ为实Ｆｒｃｈｅｔ空间，Ｋ为Ｅ的锥，本文讨论Ｅ上具有扰动的微分方程边界值问题：－ｘ＂（ｔ）＝ｆ（ｔ，ｘ（ｔ））＋ｇ（ｔ，ｘ（ｔ））ｔ∈Ｉ＝［０，１］ｘ（０）＝ｘ（１）＝θ正解的存在性，其中ｆ，ｇ∈ｃ［Ｉ×Ｋ，Ｋ］且ｆ（ｔ，θ）＝θ，ｇ（ｔ，θ）＝θ，ｔ∈Ｉ．θ为空间零元素，该文的结果主要应用作者的关于Ｆｒｃｈｅｔ空间中不动点存在定理而得，推广了它在Ｂａｎａｃｈ空间的情形，也推广了［１］的结果。

Let E be a real Frechet space, K a cone of E.In this paper, we discuss the existence of positive solutions Of boundary value problem:-x'(t) = f(t, x(t) )+g(t, x(t)) t∈ I = [0,1]x(0) = x(1) =θ,where f and g are continuous mappings from I×K into K, and f(t, θ) = θ, g(t,θ) =θ for t∈I. Us using .the fixed point theorem in [2], we prove existence theorems of positire solutions of the above Problem in Frechet spaces and generalige the main result of[1].