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I would do it this way:

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, &$wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'%' . esc_sql( $wpdb->esc_like( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = new WP_Query($args);

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, $wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'%' . esc_sql( $wpdb->esc_like( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = new WP_Query($args);

I would do it this way:

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, &$wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'' . esc_sql( $wpdb->esc_like( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = WP_Query($arg);

I would do it this way:

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, &$wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'%' . esc_sql( $wpdb->esc_like( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = new WP_Query($args);

I would do it this way:

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, &$wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'' . esc_sql( like_escape( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = WP_Query($arg);

I would do it this way:

functions.php

<?php
add_filter( 'posts_where', 'title_like_posts_where', 10, 2 );
function title_like_posts_where( $where, &$wp_query ) {
    global $wpdb;
    if ( $post_title_like = $wp_query->get( 'post_title_like' ) ) {
        $where .= ' AND ' . $wpdb->posts . '.post_title LIKE \'' . esc_sql( $wpdb->esc_like( $post_title_like ) ) . '%\'';
    }
    return $where;
}
?>

Then:

$args = array(
    'post_title_like' => $str
);
$res = WP_Query($arg);