I'm afraid that '/opt/bootlocal.sh' is not quite the right place for the start-up of an application that requires a running X server. The purpose of that file tends to be more for system-wide settings that I'd like to describe as "lower level infrastructure" (e.g. mounting of devices, specific network configuration, etc.).
Please try to create a new file in '~/.X.d' that contains the required start-up instruction (e.g. via echo 'epiphany &' > ~/.X.d/epiphany.sh, and don't forget to backup before you re-boot to test it).
PS: You should not be too concerned about the fact that English is not your first language. The same is the case for a lot of people in this forum here (myself included) and we tend to understand each other nevertheless. I believe your question was quite clear.
Edit: Sorry I only just saw now that Arslan gave you in principle the same answer, and suggested an even "better" command (as it is includes a check of the existence of the file that is to be executed).