Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
25.03.1923
Keywords: locally compact spaces; functions spaces; embedding theorems; boundary value problems; differential equations; variational method; singular points; asymptotics of solutions; extension of solutions; spaces of function with given asymptotics; almost normed spaces.
Subject:
Some results in the theory of homological groups of locally compact spaces were obtained. Investigations in the metrical and topological theories of differential mappings were carried out. The theory of embeddings for weighted functions spaces was created and, on this base, there was developed a variotional method of solving boundary value problems for elliptic equations degenerating at the boundary of the domain. The theory of almost normed spaces of functions with given asymptotics was created. Some new problems with asymptotic initial data in singular points of ordinary differential equations were formulated. Theorems of existence, uniqueness and stability of solutions were proved. The conditions have been fined when the space of solution of a linear system of differential equations is an attractor of corresponding nonlinear system.
Main publications:
L. D. Kudryavtsev, “Asymptotics of Solutions to Differential Equations near Singular Points”, Proc. Steklov Inst. Math., 232 (2001), 187–210
L. D. Kudryavtsev, “Criterion of polynomial increase of a function and its derivatives”, Anal. Math., 18:3 (1992), 223–236
L. D. Kudryavtsev, “The solution of the first boundary-value problem for self-adjoint elliptic equations in the case of an unbounded region”, Math. USSR-Izv., 1:5 (1967), 1131–1151
L. D. Kudryavtsev, “Direct and inverse imbedding theorems. Applications to the solution of elliptic equations by variational methods”, Trudy Mat. Inst. Steklov., 55, Acad. Sci. USSR, Moscow, 1959, 3–182 , 184 pp.
L. D. Kudryavtsev, “On properties of differentiable mappings of regions of Euclidian spaces”, Mat. Sb. (N.S.), 32(74):3 (1953), 493–514
