Asymptotic behavior of eigenvalues of a boundary value problem for a second order elliptic differential-operator equation with a spectral parameter linearly occurring in the boundary conditions

In the paper we study asymptotic behavior of eigenvalues of a boundary value problem for a second order elliptic differential operator equation in the case when one and the same spectral parameter participates linearly in the equation and in the boundary conditions, moreover the spectral parameter in the boundary conditions stands in front of the derivative of the desired function. Asymptotic formulas for the eigenvalues of the considered boundary value problems are found