International Journal of Nonlinear Analysis and Applications

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

Articles in Press

Document Type : Research Paper

Author

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

10.22075/ijnaa.2024.32715.4870

Abstract

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 $L^1(\Omega)$.

Keywords

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International Journal of Nonlinear Analysis and Applications

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