一类边值问题正解的确切个数

利用打靶法给出了一类边值问题x″(t)=λxα(t),t∈(0,1),x(0)=x(1)=0正解的确切个数,得到了(i)当λ<0,α>-1且α≠1时,该边值问题只有唯一的正解;(ii)当λ<0且α<-1时,该边值问题没有正解等结论.

The Exact Number of Positive Solutions for a Class of Boundary Value Problems

Using the shooting method,we discussed the exact number of positive solutions for a class of boundary value problemx″(t)=λxα(t),t∈(0,1),x(0)=x(1)=0and got the conclusion that:(i) the positive solution is unique if λ<0,α>1 and α≠1;(ii) there has no positive solution if λ<0 and α<-1.