I'm looking for the best solution for the following scenario:
CORE router is running OSPF along with R1 and R2.
R1 is border router and has working BGP session (full routes) and is directly connected to CORE router.
R2 is secondary border router, also has working BGP session (full routes) and is directly connected to CORE router.
R1 and R2 have no direct connection, use different ISP and ASs, both are connected to CORE and there's no iBGP running.
Now, I'd like to inject default route from the BGP into the OSPF, so CORE is aware of any changes on external links (R1 or R2) and uses the one that has working Internet connection.
What would be the next step? Shall I ask both ISPs to send me default routes via eBGP? Also, pointers on OSPF configuration would be appreciated.