Abstract
We prove the existence, multiplicity and nonexistence of positive radial
solutions to the following p-Laplacian equations $$
\left \{
\begin{array}{l} -\triangle_p
z_1=g_1(|x|,z_1,z_2,a,b) \
\ \text{in} \
\Omega,\\
-\triangle_p
z_2=g_2(|x|,z_1,z_2,a,b) \
\ \text{in} \
\Omega,\\ (z_1, z_2)
\rightarrow (0,0)\ \
as\ \
|x|\rightarrow
\infty,\\
\frac{\partial
z_1}{\partial n}
=\frac{\partial
z_2}{\partial n}= 0\ \
\text{on}\ \
|x|=r_0, \end{array}
\right. $$ where $\triangle_p
u=\text{div}({|\nabla
u|}^{p-2}\nabla u),\
1r_0>0\}$.