Bondarenko, B. A. Normalized systems of solutions of the polylinear vector-matrix Lame’s equations. (Russian) Zbl 0973.35048 Vopr. Vychisl. Prikl. Mat. 103, 11-20 (1997). The system of Lamé’s equations [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 \[ F_s^{p,q}(x,f)=\sum_{i=0}^{q-1}(-1)^i\binom{i+p-1}{p-1} \frac{x_1^{2i+2p-2+s}}{(2i+2p-2+s)!}\Delta^if(x_2,x_3) \] the normalized systems of quasipolynomial solutions to the polylinear vector-matrix Lamé’s equations are constructed and investigated. Reviewer: Valery Karachik (Tashkent) MSC: 35C05 Solutions to PDEs in closed form 35Q72 Other PDE from mechanics (MSC2000) 35E20 General theory of PDEs and systems of PDEs with constant coefficients 31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions 35C10 Series solutions to PDEs 33C70 Other hypergeometric functions and integrals in several variables 74B05 Classical linear elasticity Keywords:quasipolynomial solutions PDFBibTeX XMLCite \textit{B. A. Bondarenko}, Vopr. Vychisl. Prikl. Mat. 103, 11--20 (1997; Zbl 0973.35048)