Is there a way to prevent Eclipse from opening the browser when starting a Web application?

On Eclipse Juno through Oxygen, change the preferences (Window->Preferences->General->Web Browser) to add a new external web browser and set it's location as "/bin/true" (under UNIX), "/usr/bin/true" (under Mac OS Yosemite through Mojave), or "C:\Windows\System32\cmd.exe" with parameter "/c" (under Windows). Then set this as the default browser.

After this, whenever you "Run on server", Eclipse will spawn this command (which immediately succeeds) instead of touching your browser.

This isn't a per-project setting though.

No there is not. The way to do this is not click on the apllication and run as, but to click on your server and launch it(and deploy your application). Then you will get rid of browser opening.

If you run the server from the server view it won't open the browser.