Normalized systems of solutions of the polylinear vector-matrix Lame's equations (Q2743004)

The system of Lamé's equations [\textit{G. Lamé}, Leçons sur la théorie mathématique de l'élasticité des corps solides, Paris, Mallet-Bachelier, 1852] \((E\Delta+\gamma D)u(x)=0\), where \(x\in \mathbb{R}^3\), \(E\) is the unique matrix in \(\mathbb{R}^3\), \(\Delta\) is the Laplace operator, \(\gamma=\text{const}\), and \(D=(\partial x_i \partial x_j)_{\mid i,j= 1,2,3}\) is considered. On the base of quasipolynomial functions NEWLINE\[NEWLINE F_s^{p,q}(x,f)=\sum_{i=0}^{q-1}(-1)^i\binom{i+p-1}{p-1} \frac{x_1^{2i+2p-2+s}}{(2i+2p-2+s)!}\Delta^if(x_2,x_3) NEWLINE\]NEWLINE the normalized systems of quasipolynomial solutions to the polylinear vector-matrix Lamé's equations are constructed and investigated.