Aleksandr Lyapunov was a school friend of Markov and later a student of Chebyshev. He did important work on differential equations, potential theory, stability of systems and probability theory.
His work concentrated on the stability of equilibrium and motion of a mechanical system and the stability of a uniformly rotating fluid. He devised important methods of approximation. Lyapunov's methods, introduced by him in 1899, provide ways of determining the stability of sets of ordinary differential equations.
List of References (20 books/articles)
Article by: J.J. O'Connor and E.F. Robertson
Source: MacTutor History of Mathematics archive