Is the DXA-Java framework supported on WebSphere? We are using WebSphere 8.5 and the only documentation I've found references Apache Tomcat.
It should work, but we only tested ourselves on Tomcat, hence the Tomcat references in the documentation.
If you run into any issues (not related to Websphere setup or configuration) please set us know by logging them on Github https://github.com/sdl/dxa-web-application-java/issues
DXA Java works on WebSphere. You do have to take care of the class loading policy and you need to clean up some of the JARs though. Ginika recently wrote this helpful blog post about this topic: Setting Up DXA 1.7 Java Web Application on WebSphere 8.5