<form method="post" class="searchbox outline" role="search" action="<?php echo esc_url( home_url( '/' ) ); ?>">
    <input type="text" name="s" class="s" autocomplete="off" placeholder="<?php _e( 'What are you looking for?', 'gtp_translate' ); ?>" />
    <div class="results">
        <ul>
            <li><a href="#">Result</a></li>
        </ul>
    </div><!--End .results-->
    <input type="submit" name="search" value="<?php _e( 'Search', 'gtp_translate' ); ?>" />
</form><!--End header-search-->

// Ajax search box
    $('.searchbox .s').keyup(function() {
        var s = $(this).val();
        if( s.length > 0 ) {
            $.ajax( {
                type: 'post',
                url: gtp.ajaxurl,
                dataType: 'json',
                data: {
                    action: 'gtp_ajax_search',
                    s: s,
                },
                success: function(data) {
                    $('.results').show().append(data);
                }
            });
        } else {
            $('.results').hide()
        }
    });

// Ajax search
add_action( 'wp_ajax_gtp_ajax_search', 'gtp_ajax_search' );
add_action( 'wp_ajax_nopriv_gtp_ajax_search', 'gtp_ajax_search' );
function gtp_ajax_search() {
    if( isset( $_POST['s'] ) ) {
        $s = $_POST['s'];
        $args = array(
            's' => $s,
            'posts_per_page' => 5,
            'post_type' => 'products',
        );
        $results = new WP_Query( $args );
        echo json_encode( $results );
    }

    die;
}