When you apply for an advertised position or even call a company unsolicited you are likely to be considered a salesman advertising yourself. It is of course an advantage that they know what you want, but it is also a possible disadvantage since it may make them reluctant to offer you a job if it feels to mush like a sales situation.
When looking for a job, it can be a good idea also to get out there, where you meet people. Danish people are usually very willing to help the people they know and to use their network to look for opportunities for them. If you have the possibility, it can be valuable to place yourself in a situation where you continuously meet the same people. After some time, they are very likely to start a conversation with you and ask you what you do. The more people you know, who know that you are looking for a job, the bigger your network will become. And you chance of getting a job will increase.
There are many ways of expanding your network. You can for example offer to take part in activities at your children´s school or kindergarten or you can offer a helping hand in the local community or in a local club. Joining a club or a local network might be the easiest way of expanding your network. Clubs and networks are where Danish people socialize, and this is a good way to socialize with Danes. You can find clubs/associations in Esbjerg Municipality at www.explore.esbjerg.dk