Jakob and Bjarne Andersen

Searching for information on Jakob and Bjarne Andersen who came to America about 1906. The brothers were born in Stavanger, Jakob 1886 and Bjarne 1889, and the family story is that they worked on a ship and when they got to New Jersey, they jumped ship and entered the country illegally. I have been unable to locate them as mariners or even as passangers. Their father, my great grandfather, was Salve Andersen, a ship's captain and an exporter/importer. I have been unable to locate any information on him as well. I would appreciate any help of any kind.