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Existence of a solution for a strongly nonlinear elliptic perturbed problem in anisotropic Orlicz-Sobolev space | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 14، دوره 16، شماره 4، تیر 2025، صفحه 161-168 اصل مقاله (371.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33117.4928 | ||
| نویسندگان | ||
| Hakima Ouyahya* ؛ Rabab Elarabi | ||
| Equipe EDP et calcul scientifique, laboratoire de mathematiques et leurs interactions, Faculte des Sciences, Moulay Ismail University, Meknes, Morocco | ||
| تاریخ دریافت: 08 بهمن 1402، تاریخ پذیرش: 29 اسفند 1402 | ||
| چکیده | ||
| This paper is devoted to studying the existence of a solution to the 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 \ \ in\ \Omega \\ & u=0\ \ on\ \partial \Omega, \end{array} \right. \end{eqnarray} in the anisotropic Orlicz-Sobolev spaces, where A is a Leray-Lions operator $A(u)=\displaystyle\sum_{i=1}^{N}-\frac{\partial}{\partial x_{i}} (a_{i}(x,D^{i} u)),$ the Carathéodory function $g(x, s )$ is a non-linear lower order term that verify some natural growth and sign conditions, where the data $f$ is framed in anisotropic Orlicz-Sobolev spaces, and it is described by an Orlicz function that does not meet the $\Delta_2$-condition. Within this framework, we prove the existence of a weak solution for our strongly nonlinear elliptic problem. | ||
| کلیدواژه‌ها | ||
| Non-linear problem؛ anisotropic Orlicz-Sobolev spaces؛ Orlicz function؛ weak solution؛ perturbing term | ||
| مراجع | ||
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