فهرست نشریات علمی دسترسی آزاد ایران

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\begin{eqnarray}\label{P.1}\left \{\begin{array}{rl}&A(u)+g(x,u)= f \ \ {\rm in}\\Omega%[1.5ex]\\%[1ex]& u=0\ \ {\rm on}\ {\partial \Omega},\end{array}\right.\end{eqnarray}where $\Omega$ is a bounded open set of $\mathbb{R}^{N},$ $A=\sum_{|\alpha|=0}^{\infty}(-1)^{|\alpha|}D^{\alpha}\big(a_{\alpha}|D^{\alpha}u|^{p_{\alpha}(x)-2}D^{\alpha}u\big)$ 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 $L^1(\Omega)$.