| Abstract: |
| We consider problems of the form,
$\begin{equation}
\begin{cases}
- \Delta u &= \lambda K(x) f(u) \mbox { in } B_1^c, \
u(x)&=0 \mbox { on } \partial B_1, \
\end{cases}
\end{equation}$
where $B_1 ^c = \{ x\in \mathbb{R}^n: |x|>1 \}, n \geq 2$, $\lambda$ is a positive parameter, and $K: B_1 ^c \rightarrow \mathbb{R}^{+}$,
$f:(0,\infty) \rightarrow \mathbb{R}$ belong to classes of continuous functions with $K$ satisfying certain decay assumptions. For various classes of reaction terms and non radial weight functions, we will discuss the existence of positive solutions to such problems. |
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