 ## Some properties of eigenfunctions of a fourth-order differential operator with discontinuous coefficients. (Russian)статья Информация о цитировании статьи получена из Web of Science
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Дата последнего поиска статьи во внешних источниках: 16 января 2019 г.
• Автор:
• Журнал: Differential Equations
• Том: 16
• Номер: 11
• Год издания: 1981
• Издательство: Maik Nauka/Interperiodica Publishing
• Местоположение издательства: Russian Federation
• Первая страница: 1233
• Последняя страница: 1242
• Аннотация: The author considers the problem of eigenvalues and eigenfunctions of the operator Lu = (pu′′)′′ +(ru′)′ + qu, which is defined on an interval (a,b). The functions p, r, q are smooth functions in (a,b)\{x0} where x0 is a fixed point of the interval (a,b). The author proves the formula for the mean value, with center at the point x0, of the eigenfunction u which corresponds to the eigenvalue λ, and gives the estimate sum n=1 +infty (u^2(x))n/(\sqrt(lambda n))^(1+delta) = O(1) forall delta > 0. This estimate is uniform in x on every compactum in (a,b).
• Добавил в систему: Будак Александр Борисович

### Работа с статьей

  Budak A. B. Some properties of eigenfunctions of a fourth-order differential operator with discontinuous coefficients. (russian) // Differential Equations. — 1981. — Vol. 16, no. 11. — P. 1233–1242. The author considers the problem of eigenvalues and eigenfunctions of the operator Lu = (pu′′)′′ +(ru′)′ + qu, which is defined on an interval (a,b). The functions p, r, q are smooth functions in (a,b){x0} where x0 is a fixed point of the interval (a,b). The author proves the formula for the mean value, with center at the point x0, of the eigenfunction u which corresponds to the eigenvalue λ, and gives the estimate sum n=1 +infty (u2(x))n/(sqrt(lambda n))(1+delta) = O(1) forall delta > 0. This estimate is uniform in x on every compactum in (a,b).