Limit theorems for one-dimensional boundary-value problems
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.
English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 1, pp 77-90.
Citation Example: Kodlyuk T. I., Mikhailets V. A., Reva N. V. Limit theorems for one-dimensional boundary-value problems // Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 70-81.