<div class="header">
     <div class="search-container">
        <input type="text" id="search" placeholder="search-here"/>
     </div>
</div>
<div class="search-result">
   <div class="item">Result of search 1</div>
   <div class="item">Result of search 1</div>
   <div class="item">Result of search 1</div>
</div>

.header {
    position: fixed;
    top: 0;
    width: 100%; /* Get viewport width */
    height: 50px;
    background: #47c474;
    input {
         height: 100%;
         width: 100%;
         border: 0;
    }
}
.search-result {
     position: fixed;
     top: 50px; /* Calculate header's height */
     bottom: 0; /* Make full height of viewport */
     width: 100%; /* get full width of viewport */
     overflow-y: scroll;
     -webkit-overflow-scrolling: touch; /* smooth scroll */
}