LMR62421 Boost converter output voltage drops periodically
So I finally figured it out. I took for account the datasheet values (110mA @ 21V). So I checked this by supplying the backlight screen directly with 21V. The consumption was then 220m at this voltage. My booster was not intended to provide such current load. 

I have added a transistor at the output of the booster stage to limit the current provided. It works well now.

Thanks for all.