SHELL

-bash: bin/startup.sh: Permission denied

chmod u+x /usr/local/tomcat/bin/startup.sh

this gives the user permission to run the file
this should be done if for example catalina.sh also does not give permissions
in which case you change the directory in the command above by removing
the startup.sh to catalina.sh. 

permission denied while running startup.sh in linux

cd /home/***/jre/bin/
$ chmod +x java

permission denied while running startup.sh in linux

$ sudo startup.sh