方程u′′+(n-1)/rr′+r^m(u^p-u)=0的Dirichlet问题解的零点存在性讨论

The Existence of Zero Point of Solution for u′′+(n-1)/rr′+r^m(u^p-u)=0

考虑了初值问题u′′+n-1rr′+rm(up-u)=0,u(a)=α,u′(a)=0,(a>0,α>0,p>1,m>0,n∈Z+)的正解的零点存在性,用构造函数的方法,借助比较定理,得到当α充分大时,该问题的正解有有限的零点.推广了文献[1]的结论.

In this paper,the Dirichlet problem of equation u^(′′)+n-1rr~′+r^m(u^p-u)=0 is discussed.By making function and using comparison therom we get the solution to u^(′′)+n-1rr~′+r^m(u^p-u)=0,u(a)=α,u~′(a)=0(α>0,a>0,p>1,m>0,n∈Z+) have zero point when αis large enough.