On entire radial solutions of some quasilinear elliptic equations

Equations of the form
$$ \Delta u+K(|x|)|u|^{p-2}u=h(|x|),\qquad x\in \mathbb R^N,\quad N\geslant 3, $$
with $p>1$ are considered in the class of real-valued radial functions. A priori and asymptotic estimates that are best possible in the class of equations under consideration are established on the basis of a new integral identity. Existence theorems are obtained for entire radial solutions.