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Reducibility of quasiperiodic differential operators and averaging. (English. Russian original) Zbl 0566.35036
Trans. Mosc. Math. Soc. 1984, No. 2, 101-126 (1984); translation from Tr. Mosk. Mat. O.-va 46, 99-123 (1983).
The averaging problem for an elliptic operator, which is a perturbation of the divergent one, is studied. The solution of this problem is based on the concept of reducibility. The asymptotic behavior of the fundamental solution for elliptic and parabolic equations and some other problems are treated in order to illustrate the essential results.
Reviewer: V.Sobolev

35J15 Second-order elliptic equations
47F05 General theory of partial differential operators
35P05 General topics in linear spectral theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35K10 Second-order parabolic equations
49M15 Newton-type methods