Thank you for the tip.
I've got reply today and now follow the question how I can find the children (or perhaps grandchildren).
The best I can come up with is August Edward Anderson's obituary which appeared in the Stillwater, Minnesota Daily Gazette on Wedensday October 14, 1942 -- and it reads:
August E. Anderson Dies after long illness.
August Edward Anderson passed away Oct. 13, 1942 after a long illness. He was born April 16, 1860 in Sweden and came to Stillwater 63 years ago. He was married to Ida Erickson April 17, 1900.
Surviving him are his wife and five daughters; Mrs. Elmore Olson of Chatfield, Minn.; Mrs. Elvin Johnsrud of Albert Lea, Minn.; Mrs. Harry Swanson, Mildred and Alphie all of Stillwater.
Funeral services will be held Thursday afternoon at 2:30pm from the Jones Funeral Home. Rev. C.E. Benson will officiate. Interment will be made in Fairview Cemetery.
I hope this helps you on your search.