Servlet should have a mapping and cannot resolve Servlet

It's a known issue that is already fixed in the current IntelliJ IDEA version. For the older versions there is a workaround:

please open Project Structure | Modules | Web Facet and add your web.xml as Deployment Descriptor.

As a workaround, please open Project Structure -> Modules -> Web Facet and add your web.xml as Deployment Descriptor.

see image detail here