On the basis property of the eigenfunctions of the frankl problem with nonlocal evenness and oddness conditions of the second kind

摘要

The two versions of the modified Frankl problem, with non-local evenness condition of the second kind and with non-local oddness condition of the second kind has been reported. The basis property, and the minimality of eigenfunctions as depending on the parameter of the problem on the elliptic part of the domain have been discussed. The eigenfunctions and the eigenvalues of problem can be represented in the form of two series in all the Theorems. The problem has only the trivial solution on the hyperbolic part of the domain; in the elliptic part, the eigenfunctions.