Riquier problem for a nonlinear equation resolved with respect to the iterated Levi Laplacian

Abstract

Solutions are found for the nonlinear equation Δ _L ² U(x) = f(U(x)) (here, Δ _L is an infinite-dimensional Laplacian) which is solved with respect to the iterated infinite-dimensional Laplacian. The Riquier problems are stated for an equation of this sort.