In Denmark PhD positions are salaried academic faculty positions and advertised as such. Anyone interested in taking up such a position should therefore keep an eye on the link vacancies on the SDU website.
PhD positions are sometimes part of larger projects externally funded by the Independent Danish Research Fund:
or by private foundations, such as e.g. the Carlsberg Foundation:
or the Velux Foundation:
To qualify for such positions it is advisable to get in touch directly with the relevant department or research environment and potential principal investigator.