Search form does not work in my website

You’re missing the name of the search text input, so replace:

name=""

with

name="s"

Then take a look at searchform.php in the default themes, like Twenty Sixteen:

<form role="search" method="get" class="search-form" action="<?php echo esc_url( home_url( "https://wordpress.stackexchange.com/" ) ); ?>">
        <label>
                <span class="screen-reader-text"><?php echo _x( 'Search for:', 'label', 'twentysixteen' ); ?></span>
                <input type="search" class="search-field" placeholder="<?php echo esc_attr_x( 'Search &hellip;', 'placeholder', 'twentysixteen' ); ?>" value="<?php echo get_search_query(); ?>" name="s" />
        </label>
        <button type="submit" class="search-submit"><span class="screen-reader-text"><?php echo _x( 'Search', 'submit button', 'twentysixteen' ); ?></span></button>
</form>

as an example for e.g. attribute escaping.