Existence and behaviour of some radial solutions of a semilinear elliptic equation with a gradient-term

In this paper we study the existence, behaviour and approximation of some positive radial solutions $uleft( left| xright| right) $ of the equation $Delta u+frac 12xnabla u+u^p-lambda u^q=0,$ $xin {R}^n$ $forall left| xright| geq a>0$. The errors of the approximations for solution $u$ and the first derivative $u^{prime }$ are efined by the functions which can be sufficiently small $forall left|xright| geq a$