Background

Mark Aleksandrovich Krasnosel'skii was born on April 27, 1920 in Starokostiantyniv, Khmelnytskyi Oblast, Ukraine where his father worked as a construction engineer and his mother taught in an elementary school.

Education

In 1932 the Krasnosel'skii family moved to Berdyansk and in 1938 Mark entered the physico-mathematical faculty of Kiev University, which was evacuated at the beginning of World War II to Kazakhstan where it became known as the Joint Ukrainian University. He graduated in 1942, in the middle of the war, served four years in the Soviet Army, became Candidate in Science in 1948, with a dissertation on self-adjoint extensions of operators with nondense domains, before getting the title of Doctor in Science in 1950, with a thesis on investigations in Nonlinear Functional analysis.

Career

From 1946 till 1952, Mark was a Research Fellow at the Mathematical Institute of the Ukrainian Academy of Science in Kiev. From 1952 till 1967, he was Professor at Voronezh State University. He then moved to Moscow as a Senior Scientific Fellow (1967-1974) and then a Head of a Laboratory (1974-1990) at the Institute of Control Sciences of the USSR Academy of Science in Moscow. From 1990, he worked at the Institute for Information Transmission Problems of the same Academy.

Mark Krasnosel'skii's has authored or co-authored some three hundred papers and fourteen monographs, including books: "Integral operators in spaces of summable functions" (Moscow, 1966); "Approximate solutions of operator equations" (Moscow, 1969); "Geometric methods of non-linear analysis" (Moscow, 1975).

Achievements

• Mark Krasnosel'skii has contributed to nonlinear techniques are roughly classified into analytical, topological and variational methods., as well as to their application to many types of integral, differential and functional equations coming from mechanics, engineering, and control theory.
  
  Mark Krasnosel'skii was the first to investigate the functional analytical properties of fractional powers of operators, at first for self-adjoint operators and then for more general situations.
  
  Krasnosel'skii also presented many new general principles on solvability of a large variety of nonlinear equations, including one-sided estimates, cone stretching and contractions, fixed-point theorems for monotone operators and a combination of the Schauder fixed point and contraction mapping theorems that was the genesis of condensing operators. He suggested a new general method for investigating degenerate extremals in variational problems and developed qualitative methods for studying critical and bifurcation parameter values based on restricted information of nonlinear equations. such as the properties of equations linearized at zero or at infinity, which have been very useful in determining the existence of bounded or periodic solutions.

Works

More photos

• book

  • Topological Methods Theory of Nonlinear Integral Equations

    (International Series of Monographs on Pure & Applied Math...)

  • Systems With Hysteresis

    ((Universitext), (English and Russian Edition))

  • Integral operators in spaces of summable functions 1996
  • Approximate Solution of Operator Equations 1972
  • Geometrical Methods of Nonlinear Analysis

Connections

When Mark was 18 he married Sarra Belotserkovskaya (10.09.1921- 31.01.2009), they had 3 children (Veniamin, 1939; Alexandra (Alla), 1945; Alexander (Sasha), 1955). Now there are 7 grandchildren and 9 great-grandchildren.

Spouse:

Sarra Belotserkovskaya