贴的图片看不清楚，最好贴代码

public class LoginServlet extends HttpServlet {
private static final long serialVersionUID = 1L;


protected void doGet(HttpServletRequest request, HttpServletResponse response)
throws ServletException, IOException {
doPost(request, response);
}

protected void doPost(HttpServletRequest request, HttpServletResponse response)
throws ServletException, IOException {
String opType = request.getParameter("opType");


if (opType.equals("login")) {
// 获取前端页面传递过来的参数值
request.setCharacterEncoding("utf-8");
String username = request.getParameter("username");
String password = request.getParameter("password");
String usertype = request.getParameter("usertype");
HttpSession session = request.getSession();
if (usertype.equals("管理员")) {
ManagerDao managerdao = new ManagerDao();
Manager admin = managerdao.login(username, password);
if(admin!=null) {
//登录成功，保存用户会话信息，把用户登录信息保存起来，方便身份验证
session.setAttribute("admin", admin);
session.setAttribute("usertype", usertype); 
request.getRequestDispatcher("admin/index.jsp").forward(request, response);
}else {
request.setAttribute("message", "登录信息错误！");
request.getRequestDispatcher("index.jsp").forward(request, response); 
}

} else if (usertype.equals("用户")) {
UserDao userdao = new UserDao();
User user = userdao.login(username, password);
if(user!=null) {
//登录成功，保存用户会话信息，把用户登录信息保存起来，方便身份验证
session.setAttribute("user", user);
session.setAttribute("usertype", usertype); 
request.getRequestDispatcher("admin/lr/index.jsp").forward(request, response);
}else {
request.setAttribute("message", "登录信息错误！");
request.getRequestDispatcher("index.jsp").forward(request, response); 
}
}

}

}

}

<FORM name="loginform" method="post" action="LoginServlet?opType=login"> 
   <table width="100%" border="0" align="center" cellpadding="4" cellspacing="0" class="rtable">
  <tbody>
     <tr class="tr1">
            <td class="rldatee daslist"></td>
<td class="rltitle daslist">&nbsp;&nbsp;&nbsp;&nbsp;系统用户登录</td> 
         </tr>
     <tr class="tr1">
<td class="rldatee daslist">登录帐号：</td><input type=hidden name=method value="one"/>
            <td class="rltitle dotlist"><input type="text" size="30" name="username" required /></td> 
         </tr> 
         <tr class="tr1">
<td class="rldatee daslist">登录密码：</td>
            <td class="rltitle dotlist"><input type="password" size="30" name="password" required /></td> 
         </tr>
         <tr class="tr1">
<td class="rldatee daslist">用户身份：</td>
            <td class="rltitle dotlist"> 
            <input type="radio" name="usertype" value="用户" > 用户
            <input type="radio" name="usertype" value="管理员" checked> 管理员</td> 
         </tr> 
         <tr class="tr1">
            <td class="rldatee daslist"></td>
<td class="rltitle daslist"><input type="submit" value="点击登录" style="width:80px;" /> </td> 
         </tr>
         <tr class="tr1">
            <td class="rldatee daslist"></td>
<td class="rltitle daslist">&nbsp;</td> 
         </tr> 
      </tbody>
</table> 
</FORM> 

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/j2ee" xmlns:web="http://xmlns.jcp.org/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/j2ee http://java.sun.com/xml/ns/j2ee/web-app_2_4.xsd" version="2.4">
  <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>AdminServlet</servlet-name>
    <servlet-class>lx.servlet.AdminServlet</servlet-class>
  </servlet>
  <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>UserServlet</servlet-name>
    <servlet-class>lx.servlet.UserServlet</servlet-class>
  </servlet>
  <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>LoginServlet</servlet-name>
    <servlet-class>lx.servlet.LoginServlet</servlet-class>
  </servlet>
  <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>SysServlet</servlet-name>
    <servlet-class>lx.servlet.SysServlet</servlet-class>
  </servlet>
    <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>ExamServlet</servlet-name>
    <servlet-class>lx.servlet.ExamServlet</servlet-class>
  </servlet>
    <servlet>
    <description>This is the description of my J2EE component</description>
    <display-name>This is the display name of my J2EE component</display-name>
    <servlet-name>FormServlet</servlet-name>
    <servlet-class>lx.servlet.FormServlet</servlet-class>
  </servlet>
 <servlet-mapping>
    <servlet-name>AdminServlet</servlet-name>
    <url-pattern>/AdminServlet</url-pattern>
  </servlet-mapping>
  <servlet-mapping>
    <servlet-name>UserServlet</servlet-name>
    <url-pattern>/UserServlet</url-pattern>
  </servlet-mapping>
  <servlet-mapping>
    <servlet-name>LoginServlet</servlet-name>
    <url-pattern>/LoginServlet</url-pattern>
  </servlet-mapping>
  <servlet-mapping>
    <servlet-name>SysServlet</servlet-name>
    <url-pattern>/SysServlet</url-pattern>
  </servlet-mapping>
    <servlet-mapping>
    <servlet-name>ExamServlet</servlet-name>
    <url-pattern>/ExamServlet</url-pattern>
  </servlet-mapping>
    <servlet-mapping>
    <servlet-name>FormServlet</servlet-name>
    <url-pattern>/FormServlet</url-pattern>
  </servlet-mapping>
</web-app>

路径问题吧
web.xml 把loginServlet路径改下面试试。

<servlet-mapping>
    <servlet-name>LoginServlet</servlet-name>
    <url-pattern>/healthy/LoginServlet</url-pattern>
  </servlet-mapping>

可以看看浏览器是否有提示,网络请求里面应该有报错,打开调试工具看看吧

我测试下来
<servlet-mapping>
    <servlet-name>LoginServlet</servlet-name>
    <url-pattern>/LoginServlet</url-pattern>
  </servlet-mapping>

这样写是无法通过tomcat9.0部署的，
web改为
<servlet-mapping>
    <servlet-name>LoginServlet</servlet-name>
    <url-pattern>/111/LoginServlet</url-pattern>
  </servlet-mapping>

action相应改一下测试可以正常运行
<FORM name="loginform" method="post" action="111/LoginServlet?opType=login">