Comment 16 for bug 1725840

I have a similar issue on a fresh 17.10 install:
global sites are resolving OK, but local corporate sites not resolving

firther investigation:

# systemctl status systemd-resolved-update-resolvconf.service
● systemd-resolved-update-resolvconf.service
   Loaded: loaded (/lib/systemd/system/systemd-resolved-update-resolvconf.service; static; vendor preset
   Active: inactive (dead)
Condition: start condition failed at Tue 2017-12-19 14:05:37 MSK; 2 days ago
           └─ ConditionFileIsExecutable=/sbin/resolvconf was not met

# dpkg -l resolvconf
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name Version Architecture Description
+++-====================-===============-===============-=============================================
un resolvconf <none> <none> (no description available)

#apt install resolvconf

fixed the issue