on the existence of a solution for a strongly nonlinear elliptic perturbed anisotropic problem of infinite order with variable exponents

In this work, we shall be interested in the existence of a solution to the following dirichlet problem for a specific class of elliptical anisotropic equations of the type {a(u) + g(x, u) = f in ω u = 0 on ∂ω, (0.1) where ω is a bounded open set of r n, a = ∑∞ |α|=0(−1)|α|dα (aα|dαu|pα(x)−2dαu) is an operator of infinite order and g(x, s) is a non-linear lower order term that verify some natural growth and sign conditions, where the data f is framed in l^1 (ω).