Hello and thank you for your detailed suggestions, Talisien!!!!
I did what you suggested but, unfortunately, that did not solve the problem As the normal user I can do
(or use any other IP address of the form aaa.bbb.ccc.ddd) with success, but if I try
(for example www.heise.de) it fails ("unknown host www.anywhere.xyz" as I recall). But if I then do
sudo ping www.anywhere.xyz
I have success The same goes for running the links text-browser or also for firefox: www-pages can only be called up when running the programs with sudo, but when run as the normal user pages can only be accessed when the IP address is given as the URL.
So actually everything works perfectly, but only for the root user (that is, for sudo executions). And if I know the IP address, then everything also works for the normal user.
I had hopes that the rp-pppoe.so entry in pppoe.conf file would do the trick, but it was in vain. Any other suggestions