一类二阶两点边值问题正解的唯一性

Uniqueness of Positive Solutions to a Class of Second Order Two-point Boundary Value Problems

考虑一类带权函数的二阶两点边值问题■正解的唯一性,其中λ>0为参数,权函数h∈C1([0,1],R),函数f∈C1([0,∞),[0,∞))。运用分歧技巧和Sturm比较定理,获得了上述问题正解集合的全局结构,进而对于任意给定的参数λ>0,得到了该问题正解不存在或恰有一个的确切结论。

Abstract：We consider the existence and uniqueness of positive solutions to the boundary value problems{u＂＋h（t）u＇＋λf（u）=0,t∈（0,1）,u（0）=0,u/（1）=0 where λ〉0 is a positive parameter and the functions h∈C^1（[0,1],R）,F∈C＆1（[0,∞）,[0,∞））.Using bifurcation techniques and Sturm＇s comparison theorem, we determine the whole positive solution set and obtain the nonexistence or uniqueness of positive solutions to the problem for any given λ〉0.