Abstract
In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal oddness condition of the first kind in the Sobolev space $(W^{1}_{p}(0,\pi))$ . We analyze the completeness, the basis property, and the minimality of the eigenfunctions in the space $(W^{1}_{p}(0,\pi))$ .
Highlights
The classical Frankl problem was considered in [ ]
We write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal oddness condition of the first kind
We can obtain new results by the expansion into cosines that are related to new coefficients which we calculated
Summary
The classical Frankl problem was considered in [ ]. -. The modified Frankl problem with a nonlocal boundary condition of the first kind was studied in [ , ]. The basis property of eigenfunctions of the Frankl problem with nonlocal parity conditions in the Sobolev space was studied in [ ]. -. In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal oddness condition of the first kind. We can obtain new results by the expansion into cosines that are related to new coefficients which we calculated. This analysis and results may be of interest in itself. ([ ]) The eigenvalues and eigenfunctions of problem ( )-( ) can be written out in two series.
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