Existence Results for Strongly Nonlinear Elliptic Equations of Infinite Order

Abstract

In this work, generalized Sobolev spaces and Sobolev spaces of infinite order are considered. Existence of solutions for strongly nonlinear equation of infinite order of the form $Au+g(x,u)=f$ is established. Here $A$ is an elliptic operator from a functional space of Sobolev type to its dual and $g(x,s)$ is a lower order term satisfying a sign condition on $s.$