Anisotropic nonlinear problem of infinite order with variables exponents
and $L^1$ data
In this paper, we prove the existence of solutions for the strongly
nonlinear equation of the type $$Au+g(x,u)=f$$ where $A$ is an
elliptic operator of infinite order from a functional Sobolev spaces of
infinite order with variables exponents to its dual. $g(x, s)$ is a
lower order term satisfying essentially a sign condition on s and the
second term f belongs to $L^1(\Omega)$.