I have a new lawnmower and everytime I crank it up it starts on the first pull and then within 3 seconds cuts off. I found out that it I only put about a half of tank of gas in it it will stay cranked and runs fine. It does seem like when it is running that it revs up and down some but it doesn't cut off. Any ideas as to what causes this?
Not really my area but it sounds like you may have a vacuum in the gas tank. Typically (though not always) the gas caps are designed to let air in through a one way valve. One test would be to try starting it full with the gas cap cracked a little to see if the problem persists and try not to spill any thing. Or a half full see if cracking the gas cap removes the reving. You may have to get the gas cap replaced, or if you know what you're doing the vlave may just be sticking and need some work to lossen it up.
I've had that problem before, and it sounds like Sendres was correct. You have all the symtoms of that problem. You might try blowing out around the holes on the gas cap with compressed air. It seems like mine was in columns that ran up from the outside of the cap from bottom to the top. Others I have seen have a vent hole in the center of the cap. If you have an inline fuel filter that is clear, you can see if the fuel is getting that far and if it's struggling or not and at what time. If by opening the cap a little, it starts the fuel running again to the filter you can see the results there.
If none of that works, I might blow out the lines, change the fuel filter, and clean the carb, but starting with the fuel cap and finding the problem there would be a good thing.