Anatoliy Mishkis

Country: Russia
Company: Science
His mother Khaya Myshkis was born in Orhei, Bessarabia. A. D. Myshkis may be regarded by right as the founder of a number of scientific schools. His first results, obtained in 1945, were devoted to conditions for a function uniformly continuously differentiable inside a domain that is differentiable on the boundary of the domain. Later on, he established conditions underwhich a function, having al kth uniformly continuous derivatives in a domain, could be extended to Rn while preserving smoothness. Anatoly Myshkis initiated the theory of functional-differential equations in a series of papers published in 1949-1951. He was the first to denote retardedtype equa- tions. In formulating an initial-value problem, he proved theorems on the solvabili- ty of this problem for such equations and the corresponding functional-differential inclusions as well Importantly, he obtained sharp estimates about the oscillatory cha- racter and asymptotic behavior of solutions to linear equations. Later on, a number of theorems were also obtained on the solvability of and properties of solutions to boundary-value problems with several leading terms. It turned out that distributions were a natural way of defining a solution. The applicability of the difference scheme to boundary - value problems for functional-differential equations was also shown.
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