一类m-点边值问题的正解

Positive Solutions for m -Point Boundary Value Problems

研究一类二阶m-点边值问题 {u″＋f（t,u,u′）=0,0〈t〈1,u（0）=0,u（1）=∑i=1^m-2aiu（ζi） 其中，ai〉0,i=1,…,m-2,ζi满足0=ζ0〈ζ1〈ζ2〈…〈ζm-2〈ζm-1=1和∑i=1^m-2aiζi〈1。应用推广的Krasnoselskii＇s不动点定理，给出了上述边值问题至少存在一个正解的充分条件。

The paper studies the existence of positive solutions to the second order m - point boundaryvalue problem {u″＋f（t,u,u′）=0,0〈t〈1,u（0）=0,u（1）=∑i=1^m-2aiu（ζi）where ai〉0 for i=1,…,m-2,ζi satisfy 0=ζ0〈ζ1〈ζ2〈…〈ζm-2〈ζm-1=1 and ∑i=1^m-2aiζi〈1i.It provides sufficient conditions for the existence of at least one positive solution by applying the extending Krasnoselskii＇s fixed point theorem in cone.