1995 Nissan Altima car dies and acts up.

It isn't an everyday ordeal but when it the car warms up the lights will dim, the radio will start cutting out, and the tach will jump up and down, the engine will cut of and on but it hasn't died once I park it. If the lights are on it will run at less than 1,000 rpms, but if I turn the lights off it will jump to 2,000. Then when I turn it off it wont start like the battery is dead. If I let it sit overnight it will sometimes start, but mor often than naught the battery is dead. Once the battery is charged and the charging system is tested everything is normal. I have had the alternator checked and that is fine.