Radially symmetric solutions of the $p$-Laplace equation with gradient terms

We consider the Dirichlet problem for the $p$-Laplace equation with nonlinear gradient terms. In particular, these gradient terms cannot satisfy the Bernstein–Nagumo conditions. We obtain some sufficient conditions that guarantee the existence of a global bounded radially symmetric solution without any restrictions on the growth of the gradient term. Also we present some conditions on the function simulating the mass forces, which allow us to obtain a bounded radially symmetric solution under presence of an arbitrary nonlinear source.