Abstract:
In the class of continuous and continuously differentiable up to the second order functions the boundary eigenvalue problem for the Laplace operator in s-dimensional unit ball $\Omega$ with displacements in derivatives along the radii $0<r_0<1$ and 1 of the concentric spheres is considered, i.e. $u\in C^{2+\alpha}(\Omega)$ and $\frac{\partial u(r_0,\theta)}{\partial r}=\frac{\partial u(1,\theta)}{\partial r}$.
In the previous work of the authors [svmo1] were found eigenvalues and for $s=2$ eigen- and adjoint functions (Jordan chains) for the direct problem; and their length does not exceed three. In this work, calculated Jordan chains for the conjugate problem when $s=2$, the direct and conjugate problems when $s>2$, and it is proved that if $s>2$ they are terminated at the second elements
Keywords:Laplace operator, unit ball in $\R^{s+1}$, eigenvalues, eigen- and adjoint functions, Jordan chains, direct and conjugate problems for $s=2$ and $s>2$.