方程u″+((n-1)/r)u′+rm(u^p-u)=0初值问题的正解讨论

DISCUSSION OF POSITIVE SOLUTION TO THEDIRICHLET PROBLEM OF EQUATION u″+((n-1)/r)u′+r^m(u^p-u)=0

讨论了方程u″+((n-1)/r)u′+rm(up-u)=0(r>0,p>1,m∈Z+)的初值问题u′(a)=0,u(a)=α(a>0,α>0).利用能量函数及比较原理,得到了该问题的正解随初值α的变化情况.

The dirichlet problem of equation u″+((n-1)/r)u′+r^m(u^p-u)=0,p>1,m∈Z_+,u′(a)=0,u(a)=α(a>0,α>0) is discussed by means of energy function and Strum therom.Some conclusions are obtained.