ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34K10, 34B10 Bravyi, Evgenii, Perm State Technical University, Russia Correct behavior of Green’s operators of singular boundary value problems A Green’s operator of a Vallee-Poussin boundary value problem (Ax)(t) = f(t), t ∈ [a, b], x^{(i)}(a_{j}) = 0, i = 0, … n_{j} − 1, a = a_{1} < a_{2} < … < a_{k} = b, ∑_{j=1}^{k} n_{j} = n, behaves correctly, if for each non-negative function f the solution x satisfies to the inequality x(t) ∏_{j=1}^{k}(t − a_{j})^{n_{j}} ≥ 0, t ∈ [a, b]. Continuing researches of N. Azbelev, E. Chichkin, A. Domoshnitsky and S. Labovsky, we offer statements giving possibility to establish the correct behavior of Green’s operators of Vallee-Poussin boundary value problems for the n-order linear functional-differential equations with a singular factor at the higher derivative. Reference: N. Azbelev, and A. Domoshnitsky, To a question on linear differential inequalities. (Russian) Differential Equations 27, (1991), 376-384; 923-931.