Nonlinear elliptic equations of infinite order

In this work, generalized Sobolev spaces 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 operator from a Sobolev space type to its dual and g(x, s) is a lower order term satisfying a sign condition on s. We consider the case where the data f belongs to L¹.