  Lyubeznik's conjecture, (\cite{Ly1}, Remark 3.7) asserts the finiteness of
the set ssociated primes of local cohomology modules for regular rings. But, in
the case of ramified regular local ring, it is open. Recently, in Theorem 1.2
of \cite{Nu1}, it is proved that in any Noetherian regular local ring $S$ and
for a fixed ideal $J\subset S$, associated primes of local cohomology
$H^i_J(S)$ for $i\geq 0$ is finite, if it does not contain $p$. In this paper,
we use this result to construct examples of local cohomology modules for
ramified regular local ring so that they have finitely many associated primes.
