ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34, 45 Rajabov, Nusrat, Tajik State National University, Tajikistan Linear conjugate boundary value problems for the second order linear ordinary differential equation with super—singular coefficients Let Γ_{0} = {a < x < b} is set of the points on the real axis, contains the points x = b_{1}, …, x = b_{n}. Futher denote Γ_{b} = {b_{1}, b_{2}, …, b_{n}}. In Γ = Γ_{0}\Γ_{b} we shall consider the following equation

ω^{2}(x)y′′ + a_{1}(x)ω(x)y′ + a_{2}(x)y = f(x),

where ω(x) = ∏_{j=1}^{n} |x − b_{j}|^{α}, α = const > 0. On the bases obtained integral

representation in dependent from position singular points in Γ_{0}, power singularity, the roots of characteristic equation in singular points, posing and investigation of the linear conjugate boundary value problems with the set conditions in the singular points. Reference: N. Rajabov, An Introduction to The Theory of Partial Differential Equations with super–singular coefficients, Dushanbe, 1996, 230 p.