R: Cannot install rJava; what is r-api-3.4?
The API versions are provided by r-base-core. The reason is that binary packages (sometimes) depend on the R version, for which they have been build. This way you can only install packages that fit together.
In your case you have packages from the main Ubuntu repository (r-base-core 3.4.x providing r-api-3.4 and r-cran-rjava requiring r-api-3.4) and from a custom PPA (r-base-core 3.5.y providing r-api-3.5). One option would be to only use the version from Ubuntu, i.e. R 3.4. Another solution is to add an additional PPA:
sudo add-apt-repository ppa:marutter/c2d4u3.5sudo apt-get updateAfter that a version of r-cran-rjava requiring r-api-3.5 should be available.See also http://rubuntu.netlify.com/post/2018-05-25-announcing-c2d4u3-5/ and http://rubuntu.netlify.com/post/2018-06-11-r-3.5-on-debian-and-ubuntu-update/.
Finally, you always have the possibility to install the R packages directly from CRAN. That is currently the only possibility when you are using the CRAN supplied R backports on Debian.