Existence of polynomial solutions of degree 4 of the Monge-Ampère equation. Large deflections of thin plates

Abstract

We provide necessary and sufficient conditions for the solvability of a simplest Monge-Ampère equation, assuming that both the right-hand side and the solution are polynomials of degree 4. We give a constructive method of solution of the basic system of algebraic equations corresponding to the Monge-Ampère operator under the above conditions on the prescribed polynomial. Applications to large deflections of thin plates are presented. Bibliography: 9 titles.