getElementsByTagName()

 window.onload = function(){
              var oUL1 = document.getElementById("ul1");
              var oUL2 = document.getElementById("ul2");
              var oDiv = document.getElementById("div1");
                    
              oLi = getElementsByClassName(oDiv,'p', 'box');
              
              for(var i=0; i< oLi.length; i++)
              {
                  oLi[i].style.background= "red";
              }
        }
        
        function getElementsByClassName(parent, tagName, className)
        {
                 var aEls = parent.getElementsByTagName(tagName);
                 var aArr = [];             
                 for(var i=0; i< aEls.length; i++)
                 {        
                              
                      var aClass = aEls[i].className.split(" ");    
              
                        for(var j=0; j< aClass.length; j++)
                        {
                              if(aClass[j] == className)
                              {
                                  aArr.push(aEls[i]);
                                  break;
                              }                         
                        }                  
                 }
                 
            return aArr;
        }

<ul id="ul1">
    <li>111111111</li>
    <li class="box box">222222222</li>
    <li>333333333</li>
    <li class="box box1">444444444</li>
</ul>


<ul id="ul2">
    <li>111111111</li>
    <li class="box box">222222222</li>
    <li>333333333</li>
    <li class="box box1">444444444</li>
</ul>

<div id="div1">
    <p class="box">11111111</p>
</div>