Multiplicity results for some perturbed elliptic problems in unbounded domains with non-homogeneous boundary conditions

We study the following nonlinear elliptic problem $u + m u = g(x,u) + f(x)$ in $R^N \setminus \bar{B}_R$, $u = h$ on $\partial B_R$, $u \to 0$ as $jxj \to +\infty$, with $N \ge 3$, $m > 0$, under suitable conditions on the radial functions $g, f$ and $h$. Multiplicity results are proved in the perturbed case $f \not\equiv 0$ and $h \not\equiv 0$ by using Bolle's Perturbation Method and suitable growth estimates on min-max critical levels.