无界域上各向异性 Orlicz-Sobolev 空间中的准线性椭圆问题

IF 1 3区 数学 Q1 MATHEMATICS
Karol Wroński
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引用次数: 0

摘要

我们研究了一个在整个 \(\mathbb {R}^n\) 上具有各向异性凸函数 \(\Phi \)的准线性椭圆问题(-\text {div} (\nabla \Phi (\nabla u))+V(x)N'(u)=f(u))。为了证明非小弱解的存在性,我们使用了定义在各向异性奥利兹-索博列夫空间上的函数的山口定理({{\,\mathrm{textbf{W}}\,}^1}{{\,\mathrm{textbf{L}}\,}}^{\Phi }}.(\mathbb {R}^n)\).由于域是无界的,我们需要使用为 Young 函数制定的 Lions 型 Lemma。我们的假设拓宽了所考虑的函数类 \(\Phi \),因此我们的结果概括了之前在各向同性设置中证明的类似结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain

Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain

We study a quasilinear elliptic problem \(-\text {div} (\nabla \Phi (\nabla u))+V(x)N'(u)=f(u)\) with anisotropic convex function \(\Phi \) on the whole \(\mathbb {R}^n\). To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz–Sobolev space \({{{\,\mathrm{\textbf{W}}\,}}^1}{{\,\mathrm{\textbf{L}}\,}}^{{\Phi }} (\mathbb {R}^n)\). As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden the class of considered functions \(\Phi \) so our result generalizes earlier analogous results proved in isotropic setting.

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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
99
审稿时长
>12 weeks
期刊介绍: This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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