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In this paper we study results of existence and non-existence of solutionsfor the following Ambrosetti-Prodi type problem $$ \left\{ \begin{array}{lcl}-\Delta u=P(x)\Big( g(u)+f(x)\Big) \mbox{ in } \mathbb{R}^N,\\ u \inD^{1,2}(\R^N),\ \lim_{|x|\to +\infty}u(x)=0, \end{array} \right. \eqno{(P)} $$where $N\geq3$, $P\in C(\R^N,\R^+)$, $f\in C(\R^N)\cap L^{\infty}(\R^N)$ and$g\in C^1(\R)$. The main tools used are the sub-supersolution method andLeray-Schauder topological degree theory.

On an Ambrosetti-Prodi type problem in $\R^N$