  We study the following Kirchhoff equation $$- \left(1 + b \int_{\mathbb{R}^3}
|\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \ x \in \mathbb{R}^3.$$ A
special feature of this paper is that the nonlinearity $f$ and the potential
$V$ are indefinite, hence sign-changing. Under some appropriate assumptions on
$V$ and $f$, we prove the existence of two different solutions of the equation
via the Ekeland variational principle and Mountain Pass Theorem.
