二阶两点边值问题单调正解的存在性

考察了形如{x″(t)+f(t,x(t))=0,0≤t≤1,x(0)=ξx(1),x′(1)=ηx′(0)的二阶非线性微分方程两点边值问题,这里ξ,η∈(0,1)∪(1,∞)为给定的常数,f:0,1]×0,∞)→0,∞)连续。在某些适当的增长性条件下,应用Avery-Anderson-Krueger不动点定理证明了单调正解的存在性。

EXISTENCE OF MONOTONE POSITIVE SOLUTION FOR SECOND-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, the following nonlinear second-order two-point boundary value problem is considered: $$\left\{\aligned & x'(t)+f(t,x(t))=0,\quad 0\leq t\leq 1,\\&x(0)=\xi x(1),\quad x'(1)=\eta x'(0),\endaligned\right.$$where $\xi,\ \eta\in(0,1)\cup(1,\infty),\ f:0,1]\times0,\infty)\to0,\infty)$ is continuous. Under some suitable growth conditions on $f$, the existence of monotne positive solutions for the problem is proved by applying a fixed point theorem due to Avery, Anderson and Krueger.