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\begin{center}
\textbf{{\large {\ Stability of basis property of a type of problems \\[0pt]
with nonlocal perturbation of boundary conditions}}}\\[0pt]
\medskip Nurlan Imanbaev$^{1}$, Makhmud Sadybekov$^{2}$\\[0pt]
\medskip \textit{\ $^{1}$ Institute of Mathematics and Mathematical
Modeling, Kazakhstan, and }
\textit{South Kazakhstan State Pedagogical Institute, Kazakhstan}
\textit{imanbaevnur@mail.ru\\[0pt]
$^{2}$ Institute of Mathematics and Mathematical Modeling, Kazakhstan}
\textit{sadybekov@math.kz\\[0pt]
}
\end{center}
\vspace{1cm} \textbf{Abstract:} This report is devoted to a spectral problem
for a multiple differentiation operator with an integral perturbation of
boundary conditions of one type which are regular, but not strongly regular:
\begin{equation}
l(u)\equiv -u^{\prime \prime }(x)=\lambda u(x),~0