DPDA with empty stack accepts languages which satisfies prefix property.
{a,aa,aaa} - This can be accepted by pda with empty stack as well as pda with final state as pda with empty stack and final state have same power, but this won't be accepted by DPDA with empty stack.
Every string has prefix epsilon right?
so for L={anbn , n$\geq 0$}as epsilon is a prefix for every string we can't draw a DPDA with empty stack right? as the language is not following prefix property.