Searching inside a serialized array is difficult and inefficient– ie. slow. The following pure SQL will do it:
SELECT *
FROM `wp_postmeta`
WHERE `meta_key` LIKE 'daysonair'
AND `meta_value` LIKE '%thursday%'
LIMIT 0 , 100
Something like this should get WP_Query to do something similar:
$args = array(
'post_type' => 'post',
'meta_query' => array(
array(
'key' => 'daysonair',
'value' => 'thursday',
'compare' => 'LIKE',
)
)
);
$q = new WP_Query($args);
var_dump($q);
But LIKE queries with wildcards– %— are very slow. The query has to check every row in the table for a match.
Additionally, this will be prone to error as any occurance of “thursday” will match, for example, something in an attachment image alt text.
The problem is that a serialize string is a PHP construct. MySQL does not know what to do with it other than treat it like any other string.
The only really good fix, and I don’t know if it possible in you case, is to change how the data is stored in the database. If you need to search the data it should not be stored as a serialized string. Each piece of data should be stored as an independent key/value pair.