Dear I installed PHPLIST through softaculos, I have a list of subscribers with NINE THOUSAND REGISTRATIONS, I would like to know if there is a sending limit since it is installed in my domain and being sent by my server?
That will depend on your server host and any limitations they have in force.
If they limit email sending to, for example, a 1000 a day, you will need to set your limits in config.php to suit, for example:
// define the amount of emails you want to send per period. If 0, batch processing
// is disabled and messages are sent out as fast as possible
// define the length of one batch processing period, in seconds (3600 is an hour) define('MAILQUEUE_BATCH_PERIOD', 3600);
The above would send just under 1000 in a 24 hour period. 40X24 = 960