520259 Nominatim - Openstreetmap - Create a geopicker openlayers

We are useing openstreetmap. On registration our users enter thier adresses. We need now the Latitude/Longitude (out of adress) to set a marker on map. Who knows the tool Nominatim and could insert the code for us, to translate the adress into a Latitude/Longitude? Often there is no housenumber in OSM-database, means Latitude/Longitude will be not exact. In this case a additional geopicker would be needed to get the exact Latitude/Longitude (users will mark on map the exact position). This could be done with openlayers. So we need exact Latitude/Longitude, created out of Nominatim and openlayers. We don't want g**le maps api in any case. Who can solve the task?