  We study the existence of positive solutions for the following class of
scalar field problem on the hyperbolic space $$ -\Delta_{\mathbb{H}^N} u -
\lambda u = a(x) |u|^{p-1} \, u\;\;\text{in}\;\mathbb{B}^{N}, \quad u \in
H^{1}{(\mathbb{B}^{N})}, $$ where $\mathbb{B}^N$ denotes the hyperbolic space,
$1<p<2^*-1:=\frac{N+2}{N-2}$, if $N \geqslant 3; 1<p<+\infty$, if $N =
2,\;\lambda < \frac{(N-1)^2}{4}$, and $0< a\in L^\infty(\mathbb{B}^N).$ We
prove the existence of a positive solution by introducing the min-max procedure
in the spirit of Bahri-Li in the hyperbolic space and using a series of new
estimates involving interacting hyperbolic bubbles.
