I think the biggest challenge is that Arsenal (like Spurs) will not be able to compete financially with Man City, Man Utd, Liverpool, and probably even Chelsea for the foreseeable future. Whether Korenke has the money or not is irrelevant - it's clear he will not spend.
This means that they will need to find value in the transfer market and buy shrewdly to stay in the top four. On the few occasions they spend big(ish), they can't afford flops (like Liverpool buying Andy Carol, Man City's various discarded defenders, Morata at Chelsea, and half the players Man Utd have bought since Ferg left). They also need to stop the practice of letting players with value to run their contracts down and leave on a free. Even if they are sold at a loss, some money is better than none.
They will also need to dig up cheap young talent from various nooks and crannies on a regular basis.