奇异非强制非线性椭圆方程解的存在性

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-10-08 DOI:10.1007/s10231-025-01620-w

Lucio Boccardo, Luigi Orsina

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引用次数: 0

摘要

证明了下列奇异非强制非线性问题在$W_0^{1,p}(\Omega )$中正解u的存在性： $$ \left\{ \begin{array}{cl} -\textrm{div}\Big ( \frac{\Phi (x,\nabla u)}{u^{\theta \,(p-1)}} \Big ) = f(x) & \hbox {in }\Omega , \\ u > 0 & \hbox {in }\Omega , \\ u = 0 & \hbox {on }\partial \Omega . \\ \end{array} \right. $$

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Existence of solutions for singular not coercive nonlinear elliptic equations

We prove existence of positive solutions u in $W_0^{1,p}(\Omega )$ of the following singular and not coercive nonlinear problem:

$$ \left\{ \begin{array}{cl} -\textrm{div}\Big ( \frac{\Phi (x,\nabla u)}{u^{\theta \,(p-1)}} \Big ) = f(x) & \hbox {in }\Omega , \\ u > 0 & \hbox {in }\Omega , \\ u = 0 & \hbox {on }\partial \Omega . \\ \end{array} \right. $$

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

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.