Where Do I Look for a Lost Sire Last Name Thompson

Lived in/around Alfalfa Co.Oklahoma (Cherokee, Jett )1890-1900. Wife named Lulu S. Hill. Daughter of Mack Hill. Lulu Hill had 3 children by Thompson. First born, Chester,in 1907, 2nd born Otho, in 1909. Then 3rd child, Cecil, born in Newton, Harvey Co. Kansas in 1912. Then Thompson just disappeared !! In 1920's Lulu Thompson & children are in Wichita,Kansas where she remarries to William Edward Murphy. Can anyone help me ??