It should be ok.
You can check by looking for the Voltage specs on your PS4. It might be somewhere on the bottom, and you're looking for "Input voltage". For the most part, devices have a range of functional input. Outside of this, it will either not perform to it's proper standard (below the Input range) or cause damage (above the input range).
It should look like this:
This means that the voltage of 110V will work fine with your PS4.
EDIT: Since you've stated that your PS4 says the voltage range is 220-240V, this conflicts with the standard tech specs for the PS4. I would suggest taking it into an Electronics store to get the voltage tested. However, as I have previously stated, plugging it into the wall will not cause any damage to your PS4, it will simply not function to it's full capacity.