On a nonlinear equation unsolved with respect to the levy laplacian

Abstract

We propose a method for the solution of the nonlinear equationf(U(x),ΔU(x))=F(x) (Δ _L is an infinite-dimensional Laplacian, Δ _L U(x)=γ, γ≠0) unsolved with respect to the infinite-dimensional Laplacian, and for the solution of the Dirichlet problem for this equation.