Tryit Editor v2.9

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<!DOCTYPE html>
<html>
<head>
<style>
.siblings * { 
    display: block;
    border: 2px solid lightgrey;
    color: lightgrey;
    padding: 5px;
    margin: 15px;
}
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.2/jquery.min.js"></script>
<script>
$(document).ready(function(){
    $("li.start").next().css({"color": "red", "border": "2px solid red"});
});
</script>
</head>
<body>

<div style="width:500px;" class="siblings">
  <ul>ul (parent)  
    <li>li (sibling)</li>
    <li>li (sibling)</li>
    <li class="start">li (sibling with class name "start")</li>
    <li>li (the next sibling of li with class name "start")</li>
    <li>li (sibling)</li>
  </ul>   
</div>

</body>
</html>