Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol

The aim of this work is to show existence and regularity properties of equations of the form f (?) u = U (x, u (x)) on R n, in which f is a measurable function that satisfies some conditions of ellipticity and ? stands for the Laplace operator on R n. Here, we define the class of functions to which f belongs and the Hilbert space in which we will find the solution to this equation. We also give the formal definition of f (?) explaining how to understand this operator. © 2014 Mauricio Bravo Vera.