OpenJDK

In a comment under @Thilo's answer, @mobibob asked how to set JAVA_HOME in your .bash_profile on a Mac. Answer:

export JAVA_HOME=`/usr/libexec/java_home` 

This will dynamically assign to JAVA_HOME the location of the first JDK listed in the "General" tab of "Java Preferences" utility.

See Apple Technical Q&A 1170: https://developer.apple.com/library/content/qa/qa1170/_index.html

EDIT:

If you prefer parentheses to backticks for command substitution, this also works:

export JAVA_HOME=$(/usr/libexec/java_home)

I tested this answer using a clean install of High Sierra 10.13.6. All updates from Apple were installed.

The downloads of the JDKs can be found at Java Downloads. I could not correctly view this site using Safari under High Sierra. Instead, I installed and used Firefox ESR (Extend Support Release). This link for Firefox download can be successfull viewed from Safari. The file I downloaded and installed was Firefox 115.16.1esr.dmg.

I tried JDK 23 by downloading and installing jdk-23_macos-x64_bin.dmg. This was not recognized by Java. Next, I tried JDK 21 by downloading and installing jdk-21_macos-x64_bin.dmg. This was recognized by Java.

Instructions for uninstalling a JDK can be found here. Personally, I just used the Finder to move the /Library/Java/JavaVirtualMachines/jdk-23.jdk folder to the Trash.

I tested by using the simple code given below. The code was stored in the file named Simple.java.

class Simple{  
    public static void main(String args[]){  
     System.out.println("Hello Java");  
    }  
}

Example of testing is given below.

dmas-Mac:Desktop dma$ javac Simple.java 
dmas-Mac:Desktop dma$ java Simple
Hello Java

BTW, I tested JDK 23 using macOS Monterey and did not encounter the problems that occurred with High Sierra.