English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate a nonlocal boundary value spectral problem for an ordinary differential equation in an interval. Such problems arise in solving the nonlocal boundary value for partial equations by the Fourier method of variable separation. For example, they arise in solving nonstationary problems of diffusion with boundary conditions of Samarskii-Ionkin type. Or they arise in solving problems with stationary diffusion with opposite flows on a part of the interval. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is comlplete but not forming a basis. Therefore the direct applying of the Fourier method is impossible. Based on these eigenfunctions there is constructed a special system of functions that already forms the basis. However the obtained system is not already the system of the eigenfunctions of the problem. We demonstrate how this new system of functions can be used for solving a nonlocal boundary value equation on the example of the Laplace equation.

Constructing a basis from systems of eigenfunctions of one not strengthened regular boundary value problem