$D$-brane and 5th dimensions While I was looking up the 5th dimension of the Randall-Sandram model, 
I have wondered whether Kaluza Klein theory can be applied to the $D$-brane or $p$-brane.
Can the $D$-brane and $p$-brane wrapped as compactification of the dimensions?
If so, what is the main difference between $D$- and $p$-brane?
 A: The answer is yes, branes (both $D$ and $p$) can be wrapped around compactified dimensions. There is little difference between the two types of branes with regard to compactification.
A: 
Can the D-brane and p-brane wrapped as compactification of the dimensions?

String theories are consistent in 26 (bosonic string theory), 10 (superstring theories) and 11 (M-theory) dimensions. To get our world (4D) one needs to compactify the extra-dimensions. In general $D$ branes are extended $p+1$ dimensional objects with $p$ spatial and one time dimension. Obviously, if $p>d$ (here $d$ is the dimension of theory you want to get after compactification) then some of D brane dimensions are compact. For example, compactifying superstring theory to 4D we have 6 compact dimensions and if there is a brane with $p>4$ then it has some compact coordinates. So the answer on your first question is Yes.

If so, what is the main difference between D- and p-brane?

From the definition that I gave above, you see that if you want to specify the dimension of $D$ brane you call it $Dp$ brane. Now why $D$? Actually there are two other types of branes - $NS$ and $M$ branes, so that is why we need a letter $D$ - to distinguish different types of branes.
