On Some Nonlinear Elliptic Problems with Large Monotonocity in Musielak–Orlicz–Sobolev Spaces
DOI:
https://doi.org/10.15407/mag18.03.332Анотація
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-умоваПосилання
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