There are four case make the overlap exists
(ns, ne, es, ee) = (new_start, new_end, existing_start, existing_end):

1. ns - ne - es - ee: doesn't overlap and doesn't match (because ne < es)
2. ns - es - ne - ee: ovarlaps and matches
3. es - ns - ee - ne: ovarlaps and matches
4. es - ee - ns - ne: doesn't overlap and doesn't match (because ns > ee)
5. es - ns - ne - ee: ovarlaps and matches
6. ns - es - ee - ne: ovarlaps and matches

SQL Statment Below method is found from internet while the second method is my own way usally use.

SELECT * FROM tbl WHERE
existing_start BETWEEN '$newStart' AND '$newEnd' OR
existing_end BETWEEN '$newStart' AND '$newEnd' OR
'$newStart' BETWEEN existing_star AND existing_end

SELECT * FROM tbl WHERE
( existing_start<='$newStart' AND existing_end>'$newStart' )
AND ( existing_start<'$newEnd' AND existing_start>'$newStart' )