When cooled, my browies are very sticky and hard towards the edges. What are the possible reasons that this is happening?
I think you are trying to make a more chewy brownie, and your got a quite like hard and cookie like at the bottoms. 

Dark brown sugar contains more molasses than in light brown sugar then in white sugar. Molasses is hygroscopic which means it holds on to moisture and so using brown sugar will result in baked goods that are softer and moister. But if your brownie bottom is hard, it is not the problem of lacking for moisture in your brownie mix (not brown sugar problem making the brownie hard). And if the centre of the brownie is the type of cake you need, then the reciepe is ok.

I would suggest:


Use a suitable baking pan size(diameter) that could make your brownie batter is of certain thickness (else your brownie maybe overbaked and becomes hard, if the brownie mix are too thin in the pan) 
Butter (or spray with a nonstick cooking spray) an your baking pan, and line the bottom of the pan with parchment or wax paper.