<form name="login-form" class="login-form" action="authcheck" method="post">

@WebServlet(name = "AuthCheck", urlPatterns = {"/authcheck"})
public class AuthCheck extends HttpServlet {

    private static final String CONTENT_TYPE = "text/html; charset=utf-8";
    @EJB
    private SessionEJBLocal sel;

    @Override
    protected void doPost(HttpServletRequest request, HttpServletResponse response)
            throws ServletException, IOException {
...

HTTP Status 404 - Not Found

Severe:   Class [ Lbeans/SessionEJBLocal; ] not found. Error while loading [ class start.AuthCheck ]