I want to execute a shell script when a Alpine Docker container starts up.
You should create a shell file to be copied inside a new container and then setup the container entrypoint as the shell script you created, synthax would be like
FROM <docker/alpine-image>
#.... somecode
USER root
COPY /localmachinelocation/entrypoint.sh /containerlocation/entrypoint.sh
RUN chmod 544 /var/www/webapp/entrypoint.sh
#.... somecode
CMD /containerlocation/entrypoint.sh
You could specify the user you need to run the script. Chmod ensure the script would be runnable by the owner of the script, you could change it for security matters.
Let's say you have your script in /home/user/script.sh, you could do
FROM <docker/alpine-image>
USER root
COPY /home/user/script.sh /root/entrypoint.sh
RUN chmod 544 /var/www/webapp/entrypoint.sh
CMD /root/entrypoint.sh