  In this paper we prove that the equation $ -( r^\alpha\phi(|u'(r)|)u'(r))' =
\lambda r^\gamma f(u(r)), ~0<r<R$, where $\alpha, \gamma, {\bf{R}}$ are given
real numbers, $\phi : (0, \infty) \to (0, \infty)$ is a suitable twice
differentiable function, $\lambda > 0$ is a real parameter and
$f:{\bf{R}}\to{\bf{R}}$ is continuous, admits an infinite sequence of
sign-changing solutions satisfying $u'(0) =u(R) =0$. The function $f$ is
required to satisfy $tf(t)>0$ for $ t\neq 0$. Our technique explores fixed
point arguments applied to suitable integral equations and shooting arguments.
Our main result extends earlier ones in the case $\phi$ is in the form $\phi(t)
= |t|^{\beta}$ for an appropriate constant $\gamma$.
