Abstract

The boundary value problem $$ -y''+q(x)y=\lambda y+\int_0^{\pi}y\,d\sigma(x),\quad y(0)=y(\pi)=0, $$ is concerned, where $q\in C[0,\pi]$ and $\sigma$ is a function of bounded variation. It is proved that the system of eigenfunctions of the given problem is complete and minimal in $L^2(0,\pi)$, and also that functions of a certain class can be expanded into uniformly convergent series with respect to the mentioned system.

Keywords: Functional differential equation, boundary value problem, expansion theorem.

MSC: 34K10, 47E05

Pages:  11$-$17     

Volume  45 ,  Issue  1$-$4 ,  1993