Yurii Sokolov was born in Labinskaya Stanitsa, a name of the town whose name means Cossack village. He graduated from Kiev Institute of Peoples Education in 1921 and then he taught in the Spplied Mathematics Division of the Academy.
From 1934 he taught at the Institute of Mathematics at the Academy of Sciences of Ukraine. He also taught at several other higher educational institutions in Kiev.
Sokolov's main work was on the n-body problem, which he worked on for nearly 50 years. He also worked on functional equations and on such practical problems as the filtration of groundwater. Other work by Sokolov was on celestial mechanics and hydromechanics.
One of the topics which will always be associated with
Sokolov's name is a method for finding approximate solutions to differential and
integral equations. The
method which he introduced is now sometimes called the averaging method with
functional corrections, sometimes called the Sokolov method. His methods were
highly practical and useful in many applications to mathematical physics, but
they were also studied with the highest degree of rigour.