Does eclipse Neon support Java 9?
It depends what you mean by "support". If you mean "Is the use of Java 9 officially supported with Neon?" then the answer is no. For example, see this DZone article:
You need an Oxygen-based install of Eclipse – ensure you’re using the
R version and not milestone or integration builds.
Also, from Eclipse's site:
Users who install Eclipse Oxygen 4.7.1a are able to launch with Java 9
and get Java 9 support
But if you mean "Is it possible to get Java 9 running under Neon?" then the answer is yes. Here's a snippet from an article titled Eclipse Java™ 9 Support (BETA) for Neon from a brave soul who did it back in 2015!...
I downloaded the early access version of Java 9 JDK from java.net in
the form of a tar.gz file that I decompressed into a local directory:
/home/apps/jdk1.9.0. I made no other changes to my system.
I downloaded the Eclipse SDK 4.6 (Neon) M2 from the Eclipse Platform
downloads and decompressed it into its own directory. I made a small
change to the eclipse.ini file to make the new configuration run using
the Java 9 runtime...
Of course, that was done with an early access release of Java 9, and I wouldn't automatically assume that Neon will still work with the latest release of Java 9.
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Update:
I just noticed this SO question titled Neon: how to run on jdk9? which may offer further useful information.