Display number of posts via adress bar?

If you’re asking to change the number of posts from 10 to something else, you can do one of the following

1) Submit the search query as

?s=key&order=ASC&posts_per_page=5

You can achieve this by adding hidden fields to the form. Just change the number to whatever you want

2) Go to Settings > Reading, change the setting there. This will change the setting for all the pages though

3) Add this to your theme’s functions.php or in a plugin

add_filter('pre_get_posts', 'change_posts_on_search');
function change_posts_on_search($query) {
    if($query->is_main_query() && $query->is_search())
        $query->set('posts_per_page', 5); // change the number here
}

UPDATE IN RESPONSE TO COMMENT

<form action="<?php echo home_url( "https://wordpress.stackexchange.com/" ); ?>" method="get">
    <input type="text" name="s" />
    <select name="posts_per_page">
        <option>5</option>
        <option>10</option>
        <option>15</option>
        <option>20</option>
    </select>
    <input type="submit" />
</form>

This form does that work. Basically it’s same as the first option above. But except for the hidden field, it shows the field to the user allowing for changes.