Regular boundary value problem with a spectral parameter in the boundary condition.

We consider a regular boundary value problem for the formally selfadjoint ordinary differential operator of arbitrary order. The operator is defined on the space of vector functions and the boundary condition contains the eigenvalue parameter. This problem is adequate to the eigenvalue problem for a selfadjoint operator in a wider Pontryagin space $\Pi_\kappa$. The expansion on eigenfunctions and adjoint functions is obtained. The dependence between $\kappa$ and the polynomials in the boundary condition is investigated.