  We consider degenerated nonlinear PDE of elliptic type: $$
  - \mathrm{div}(a(|x|)|\nabla w(x)|^{p-2} \nabla w(x)) +
h(|x|,w(x),\langle\nabla w(x),\frac{x}{|x|}\rangle)=\phi(w(x)), $$ where $x$
belongs to the ball in $\bf{R}^n$. Using the argument based on Opial-type
inequalities, we investigate qualitative properties of their radial solutions,
like e.g. maximum principles, monotonicity, as well as nonexistence of the
nontrivial solutions.
