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\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).

کلیدواژه های On the existence of a solution for a strongly nonlinear elliptic perturbed anisotropic problem of infinite order with variable exponents:

Strongly nonlinear elliptic equations of infinite order ، monotonicity condition ، variable exponents ، sign condition