Look at it this way:

Bende senin özlemin var

´With me there is your yearning´. It looks like ´you´ is the one that is ´yearning´, but quite the opposite is meant.

For example:

Yokluðun var

You have absence

Bende yokluðun var

I (suffer from) have your absence with me.

If anyone can help I would appreciate it

How is ´Özlemin" literally broken down?

Özle = yearning (noun?)

Özlem = my yearning

Özlemin= my yearnings?   what is the ´in´ suffix  from/for?

Senin ozlemin var  = I long for you (eng interpretation)  but could it be explained as the english interpretation of:  you have my yearnings,    

as in other english interpreted sentences when someone would say,

1. " you have my condolances´ 

or 2.  "you have my heart"?

Would those 2 sentences be constructed the same way as Senin özlemin var?

The noun is özlem, not özle.

So there is no ´my´ in it

özlem

senin özlem-in

benim özlem-im

Good explanation

The noun is özlem, not özle.

Ahh see Thank YOU for clarifying much appreciated