public static class MySqlConnector {

    private static Connection conn;

    public static synchronized Connection getConnection(String connUrl) throws ClassNotFoundException, SQLException {
        if (conn == null || (conn != null && conn.isClosed())) {
            Class.forName("com.mysql.jdbc.Driver");
            conn = DriverManager.getConnection(connUrl);
        }
        return conn;
    }
}
...
...
...
Connection conn = MySqlConnector.getConnection("jdbc:mysql://localhost/test");
ResultSet rs = conn.createStatement().executeQuery("...");
while (rs.next()) {
    System.out.println(rs.getString(1));
}
rs.close();
...

for (int i = 1; i <= 5; i++) {
    final String threadName = "Thread #" + i;
    new Thread(new Runnable() {
        @Override
        public void run() {
            while (true) {
                try {
                    Statement stmt = MySqlConnector.getConnection("jdbc:mysql://localhost/test").createStatement(); 
                    ResultSet rs = stmt.executeQuery("show variables");
                    while (rs.next()) {
                        System.out.println(threadName + ": " + rs.getString(1));
                    }
                    rs.close();
                    stmt.close();
                } catch (Exception e) {
                    e.printStackTrace(System.out);
                }
            }
        }
    }).start();
}

public void method3(....){
   synchronized(mConnection){
         method1(...)
   }
}