<div data-role=page">
    <form method="post">
        <input name="search" id="search" value="" placeholder="Buscar" type="search" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Buscar'">
    </form>
</div>

<div data-role=page">
<form method="post">
<input style='border:1px solid red;' name="search" id="search" value=""  placeholder="Buscar" type="search" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Buscar'">
</form>
</div>

<form method="post">
    <input name="search" id="search" value="" placeholder="Buscar" type="search" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Buscar'" />
</form>

var s = '<span class="fakeSearchButton"></span>';
$("#search").parents(".ui-input-search").append(s);

$(document).on("click", ".fakeSearchButton", function(){
    alert("search icon click");
});

.fakeSearchButton{
    position: absolute;
    display: block;
    height: 14px;
    left: 0.3215em;
    top: 50%;
    margin-top: -7px;
    width: 14px;
    z-index: 200;
}

.ui-input-search {
  border-color: #7FAF1B !important;
  -webkit-box-shadow:rgb(217,255,169) 0px 1px 2px 0px inset;
  box-shadow:rgb(217,255,169) 0px 1px 2px 0px inset;
}