Existence results for nonlinear elliptic $\overrightarrow{p}(\cdot)-$equations

Naceri, Mokhtar

doi:10.22034/cmde.2024.61426.2644

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	Existence results for nonlinear elliptic $\overrightarrow{p}(\cdot)-$equations
Computational Methods for Differential Equations
مقاله 16، دوره 14، شماره 1، فروردین 2026، صفحه 235-246 اصل مقاله (410.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61426.2644
نویسنده
Mokhtar Naceri^*
ENS of Laghouat; Box 4033 Station post avenue of Martyrs, Laghouat, Algeria.
چکیده
This paper investigates the existence of distributional solutions for a class of nonlinear elliptic $\overrightarrow{p}(\cdot)-$equations, the analysis focuses on the right-hand side, which comprises of a datum $f\in L^{\overrightarrow{p'}(\cdot)}(\Omega)$ that is independent of $u$, and a compound nonlinear term involving a given function $g \in L^{\overrightarrow{p}(\cdot)}(\Omega)$, the solution $u$ and its partial derivatives $\partial_iu,\,i\in\{1,\ldots,N\}$, where $L^{\overrightarrow{p}(\cdot)}(\Omega)$ and $L^{\overrightarrow{p'}(\cdot)}(\Omega)$ represent the variable exponents anisotropic Lebesgue spaces.
کلیدواژه‌ها
Variable exponent؛ Nonlinear elliptic equation؛ Anisotropic Lebesgue-Sobolev space؛ Distributional solution؛ Existence؛ Compound nonlinearity

مراجع
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Existence results for nonlinear elliptic $\overrightarrow{p}(\cdot)-$equations