Cellular network problem (Edge)-Only on my iPhone 5

Hi,

I have a problem.

With my iPhone 5, when 3G is enabled, no worries, the cellular works well.

By cons, if I disable the 3G or the iPhone only picks up the EDGE network and if the level is less than 3/5 I see "Network unavailable" .. But, if the EDGE network is more than 3/5, EDGE works ..

I can see the reception level because when it switches on any EDGE antenna , I see the level during 1-2 seconds with the "E" and then, later, no 3G or E logo appears, the iPhone displays 1/5 bar , then "Network unavailable" to a 3G antenna is detected ..

My line is properly enabled on my iPhone 4S in the same place, no worries .. I'm 5.0.1 on my iPhone 4S ...

You think it's a bug with my iPhone 5? iOs 6 which detects the level of the EDGE is too bad with less when they are 3/5 bar ?

I've called the Apple Care support, they asked me to restore as "New iPhone". Same problem with no iCloud backup and with "New iPhone" after the restore..

Anybody has got the same problem ?

Thank you so much in advance !