Mark Krasnoselsky

Mark Krasnoselsky was born in Starokostiantyniv, where his father worked as a construction engineer and his mother taught in an elementary school.

Mark Krasnoselsky has contributed to all three aspects in a significant way, as well as to their application to many types of integral, differential and functional equations coming from mechanics, engineering, and control theory.

His theorem on the interpolation of complete continuity of such fractional power operators has been a basic tool in the theory of partial differential equations.

Of comparable importance in applications is his extensive collection of works on the theory of positive operators, in particular results in which spectral gaps were estimated.

Krasnoselsky 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.