Construction of Asymptotic Formulas for Solutions of One Differential Problem with a Singular Coefficient
Tóm tắt
The first boundary value problem for a second–order differential
operator with a singular potential on a segment with conjugation
conditions at an interior point of the segment is studied. For the
solution of the problem with a parameter, asymptotic formulae and
estimates are obtained on each of the segments of smoothness. A
similar formula is obtained for the solution of the associated
problem.
Tài liệu tham khảo
O. V. Belyantsev, ‘‘The Bessel inequality and the basis property of root functions of a second–order singular differential operator,’’ Differ. Equat. 36, 1019–1030 (2000).
I. S. Lomov, Spectral Method of V. A. Ilyin. Non-Self-Adjoint Operators. I. Operator of the Second Order. Basis Property and Uniform Convergence of Spectral Expansions (MAKS Press, Moscow, 2019) [in Russian].
V. A. Il’in, Spectral Theory of Differential Operators: Self-Adjoint Differential Operators (Nauka, Moscow, 1991; Springer, New York, 1995).
O. V. Belyantsev and I. S. Lomov, ‘‘On the basis property of eigenfunctions of a singular second-order differential operator,’’ Differ. Equat. 48, 1174–1176 (2012).
L. A. Zhornitskaya and V. S. Serov, ‘‘A uniqueness theorem for the Sturm–Liouville operator on a segment with a potential that has a nonintegrable singularity,’’ Differ. Equat. 29, 1865–1864 (1993).
L. V. Kritskov, ‘‘Estimates for root functions of a singular second–order differential operator,’’ in Functional Analysis in Interdisciplinary Applications, FAIA, Astana, Kazakhstan, October 2017, Ed. by T. S. Kalmenov, E. D. Nursultanov, M. V. Ruzhansky, and M. A. Sadybekov, Vol. 216 of Springer Proceedings in Mathematics and Statistics (Springer Cham, 2017), pp. 245–257.
I. S. Lomov, ‘‘A theorem on the unconditional basis property of the root vectors of loaded second-order differential operators,’’ Differ. Equat. 27, 1098–1107 (1991).