Approximation properties of multipoint boundary-value problems - Masliuk, H.; Pelekhata, O.; Soldatov, V. (Methods of Functional Analysis and Topology, 2020)
We consider a wide class of linear boundary-value problems for systems of r-th order ordinary differential equations whose solutions range over the normed complex space (C^(n))^m of n≥ r times continuously differentiable functions y:[a,b]→C^m. The boundary conditions for these problems are of the most general form By=q, where B is an arbitrary continuous linear operator from (C^(n))^m to C^rm. We prove that the solutions to the considered problems can be approximated in (C^(n))^m by solutions to some multipoint boundary-value problems. The latter problems do not depend on the right-hand sides of the considered problem and are built explicitly.