$R_{\delta}$-set of solutions to a boundary value problem

Abstract

In the paper a sufficient condition for the existence of an $R_{\delta}$-set of solutions to a generalized boundary value problem on a compact interval is established. The proof is based on the Browder-Gupta theorem on the existence of an $R_{\delta}$-set of solutions of an operator equation and on the relation between boundary value problems and Fredholm operators. Similar result is obtained by means of the Vidossich theorem.