I have tried to install Elementary OS on my external hard drive (1TB, USB3.0).
My computer is using UEFI and is alredy dual booting Ubuntu MATE and Windows 10.
I created a Live USB with UNetbootin, and installed Elementary to my external hard drive from it. I choose something else, choose my partition to mount as / (/dev/sdc2) and choose to install grub on my hard drive (/dev/sdc), and created an efi partition, with esp and boot flags(/dev/sdc4) It installed sucessfully. When I reboot, I choose to boot to my hard drive from f12 boot menu, and I have got the "grub>" minimal bash-like command line. I followed the instruction on this post : Launchpad bug. I have been able to have the grub menu of elementary and to boot on it. Then the elementary logo appears and then I fall in a ash shell, exactly like in this post : Same problem, but no working answer is posted here.
I have tried before without EFT partition. Then I reboot and from bios boot menu f12, there was no option for my hard drive. Legacy is not working on my computer.
I also tried to run boot repair but it doesn't work either.
I though that mabe the problem is that my partition table is msdos and not gpt.