On Some Nonlinear Elliptic Problems with Large Monotonocity in Musielak–Orlicz–Sobolev Spaces

Автор(и)

  • Ouidad Azraibi Laboratory LAMA, Department of Mathematics, Faculty of Sciences Fez, Sidi Mohamed Ben Abdellah University, P.O. Box 1796 Atlas Fez, Morocco
  • Badr El Haji Laboratory LaR2A, Dpartement of Mathematics, Faculty of Sciences Tetouan, Abdelmalek Essaadi University , BP 2121, Tetouan, Morocco
  • Mounir Mekkour Laboratory LAMA, Department of Mathematics, Faculty of Sciences Fez, Sidi Mohamed Ben Abdellah University, P.O. Box 1796 Atlas Fez, Morocco

DOI:

https://doi.org/10.15407/mag18.03.332

Анотація

У цiй роботi ми вивчаємо iснування ентропiйного розв’язку деякої нелiнiйної елiптичної проблеми типу Лерея–Лiонса, пов’язану з рiвнянням $-\mathop{\mathrm{div}} a(x,u,\nabla u)=f(x)-\mathop{\mathrm{div}} F(u)$ в $\Omega$ з умовою великої монотонностi у визначеннi просторiв Мусйелака–Орлича–Соболєва, де права частина $f$ належить $L^1(\Omega)$ i $F=(F_1,...,F_N )$ задовольняє умову $F\in(C^0(\mathbb{R}))^N$.

Mathematical Subject Classification 2010: 35J62, 35J25

Ключові слова:

елiптична проблема, ентропiйний розв’язок, простори Мусйелака–Орлича–Соболєва, компактне вкладення, ∆2-умова

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Azraibi, O.; Haji, B. E. .; Mekkour, M. . On Some Nonlinear Elliptic Problems with Large Monotonocity in Musielak–Orlicz–Sobolev Spaces. Журн. мат. фіз. анал. геом. 2022, 18, 332-349.

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