Question

Suppose p>k, Dose the global solution of the following ODE exsit? ${n-1 \choose k-1} u''(r)(\frac{u'(r)}{r})^{k-1}+{{n-1} \choose k }(\frac{u'(r)}{r})^{k}=(u(r))^p$,r>0,

u(0) = a > 0,

$u\in C^2(0,\infty) \cap C[0,\infty).$

thanks~