Limit theorems for one-dimensional boundary-value problems

  • T. I. Kodlyuk
  • V. A. Mikhailets
  • N. V. Reva

Abstract

We study the limit with respect to a parameter in the uniform norm for solutions of general boundary-value problems for systems of linear ordinary differential equations of the first order. A generalization of the Kiguradze theorem (1987) to these problems is obtained. The conditions on the asymptotic behavior of the coefficients of the systems are weakened as much as possible. Sufficient conditions for the Green matrices to converge uniformly to the Green matrix of the limit boundary-value problem are found as well.
Published
25.01.2013
How to Cite
KodlyukT. I., MikhailetsV. A., and RevaN. V. “Limit Theorems for One-Dimensional Boundary-Value Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 1, Jan. 2013, pp. 70-81, http://umj.imath.kiev.ua/index.php/umj/article/view/2405.
Section
Research articles