Necessary and Sufficient Conditions for the Solvability of Linear Boundary-Value Problems for the Fredholm Integrodifferential Equations
AbstractWe propose a method for the investigation and solution of linear boundary-value problems for the Fredholm integrodifferential equations based on the partition of the interval and introduction of additional parameters. Every partition of the interval is associated with a homogeneous Fredholm integral equation of the second kind. The definition of regular partitions is presented. It is shown that the set of regular partitions is nonempty. A criterion for the solvability of the analyzed problem is established and an algorithm for finding its solutions is constructed.
How to Cite
DzhumabaevD. S. “Necessary and Sufficient Conditions for the Solvability of Linear Boundary-Value Problems for the Fredholm Integrodifferential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 8, Aug. 2014, pp. 1074–1091, http://umj.imath.kiev.ua/index.php/umj/article/view/2200.