The relationship between public debt, growth and volatility is investigated in a Barro-type (1990) endogenous growth model, with three main features: we consider a small open economy, international borrowing is constrained and households have taste for domestic public debt. Therefore, capital, public debt and the international asset are not perfect substitutes and the economy is characterized by an investment multiplier. Whatever the level of the debt-output ratio, the existing BGP features expectation-driven fluctuations. If the debt-output ratio is low enough, there is also a second BGP with a lower growth rate. Hence, lower debt does not stabilize the economy with credit market imperfections. However, a high enough taste for domestic public debt may rule out the BGP with lower growth. This means that if the share of public debt hold by domestic households is high enough, global indeterminacy does not occur.