wp_query check if integer exists in custom field’s array

First of all, your meta_query is wrong. It should be an array of an array, not just an array

So, the following

'meta_query' => array (
    'key' => 'qd_resource_author_selector',
    'value' => $myAuthor,
),

becomes

'meta_query' => array (
    array(
        'key' => 'qd_resource_author_selector',
        'value' => $myAuthor,
    ),
),

Secondly, you can optimize your query. You are running a query for every value. If you have 100 values, you are going to run 100 queries which is expensive

You can optimize your query by adding your values in an array and passing the array directly to your meta_query

Just a few other concerns

• Run a proper tax_query. The syntax you are using is depreciated

• Your first instance of get_the_title() looks out of place outside the loop. Not sure what you are doing there

• Do not mix your syntax, it is confusing and really hard to debug on failure. For your if statement you are using curlies (which I prefer as basically all editors support them, very easy to debug) and in your while statement you use : and endwhile. I would recommend that you use curlies and stick with them in future

With all said, you can try something like this without a foreach loop

$myAuthor = array('value1', 'value2', 'value3');
$args = array(
    'posts_per_page' => -1,
    'post_type' => 'resource',
    'tax_query' => array(
        array(
            'taxonomy' => 'resource_types',
            'field'    => 'slug',
            'terms'    => 'ml-special-reports',
        ),
    ),
    'meta_query' => array (
        array(
            'key'       => 'qd_resource_author_selector',
            'value'     => $myAuthor,
            'compare'   => 'IN',
        ),
    ),
    'orderby' => 'title',
    'order' => 'ASC'
);
$query = new WP_Query( $args );
if ( $query->have_posts() ) { 
    while ( $query->have_posts() ) {
        $query->the_post();
        echo '<h3>'.get_the_title().'</h3>';
    }
    wp_reset_postdata();
}