The eigenvalue problem for the Laplace operator in $s$-dimensional unit ball $\Omega$ with displacement in derivatives

In the class of continuous and continuously differentiable up to second order functions it is considered the eigenvalue problem for the Laplace operator in $s$-dimensional unit ball $\Omega$ with displacement in derivatives along radii of concentric spheres $S_{r_0}$, $0<r_0<1$, and $S_1$, $u\in C^{2+\alpha}(\Omega)$ and $\frac{\partial u(r_0,\Theta)}{\partial r}=\frac{\partial u(1,\Theta)}{\partial r}$. The relevant eigenvalues are determined and when $s=2$ it is moved the length of the corresponding Jordan chains not exceeded three. At the usage of handbooks [1, 3, 4] the conditions of their existence are obtained and their computations are made. Note, that in the works [5, 6] the analogous problem with displacements in functions was solved.