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On the existence of a solution for a strongly nonlinear elliptic perturbed anisotropic problem of infinite order with variable exponents | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 5، دوره 16، شماره 3، خرداد 2025، صفحه 53-62 اصل مقاله (365.61 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.32715.4870 | ||
| نویسنده | ||
| Hakima Ouyahya* | ||
| Equipe EDP et Calcul Scientifique, Laboratoire de Mathematiques et Leurs Interactions, Faculte des Sciences, Moulay Ismail University, Meknes, Morocco | ||
| تاریخ دریافت: 29 آذر 1402، تاریخ بازنگری: 27 دی 1402، تاریخ پذیرش: 29 دی 1402 | ||
| چکیده | ||
| 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 $L^1(\Omega)$. | ||
| کلیدواژهها | ||
| Strongly nonlinear elliptic equations of infinite order؛ monotonicity condition؛ variable exponents؛ sign condition | ||
| مراجع | ||
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