function bpd_ajax_filter_search_callback() {
  if(isset($_POST['search'])) {
    $searchterm = esc_attr( $_POST['search'] );
    $args = array(
      'posts_per_page' => -1,
      'post_status' => 'publish',
      'post_type' => 'product',
      's'   => $searchterm
    );
  }

  $the_query = new WP_Query($args);

  if($the_query->have_posts()):
      while($the_query->have_posts()):
          $the_query->the_post();
          the_title();
          echo '<br>';
      endwhile;
      wp_reset_query();
  endif;

  die;
}