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

Document Type : Research Paper


Equipe EDP et Calcul Scientifique, Laboratoire de Mathematiques et Leurs Interactions, Faculte des Sciences, Moulay Ismail University, Meknes, Morocco



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
\left \{\begin{array}{rl}
&A(u)+g(x,u)= f \ \ {\rm in}\
& u=0\ \ {\rm on}\ {\partial \Omega},
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 $L^1(\Omega)$.


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Articles in Press, Corrected Proof
Available Online from 05 March 2024
  • Receive Date: 20 December 2023
  • Revise Date: 17 January 2024
  • Accept Date: 19 January 2024