arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 0811.3292math.AP
收藏

关于两个源项为0或1阶的拟线性椭圆问题之间的联系

On the connection between two quasilinear elliptic problems with source terms of order 0 or 1

Haydar Abdel Hamid, Marie-Françoise Bidaut-Véron

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

在$\mathbb{R}^{N}.$的一个有界区域中，我们建立了两个Dirichlet数据椭圆拟线性问题之间的精确联系。第一个问题的形式为\[ -Δ_{p}u=β(u)| \nabla u| ^{p}+λf(x)+α, \]，它涉及一个自然增长的源梯度项，其中$β$是非负的，$λ>0,f(x)\geqq0$，$α$是非负测度。第二个形式为\[ -Δ_{p}v=λf(x)(1+g(v))^{p-1}+μ, \]，表示$0, $阶的源项，其中$g$是非减的，$μ$是非负的测度。此处，$β$和$g$可呈现渐近线。这种关联给出了这两个问题解的存在性、不存在性、正则性和多解性的新结果，无论有无测度。当$g$为超线性时，给出了关于极值解的新信息.

英文摘要：

We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of $\mathbb{R}^{N}.$ The first one, of the form \[ -Δ_{p}u=β(u)| \nabla u| ^{p}+λf(x)+α, \] involves a source gradient term with natural growth, where $β$ is nonnegative, $λ>0,f(x)\geqq0$, and $α$ is a nonnegative measure. The second one, of the form \[ -Δ_{p}v=λf(x)(1+g(v))^{p-1}+μ, \] presents a source term of order $0, $where $g$ is nondecreasing, and $μ$ is a nonnegative measure. Here $β$ and $g$ can present an asymptote. The correlation gives new results of existence, nonexistence, regularity and multiplicity of the solutions for the two problems, without or with measures. New informations on the extremal solutions are given when $g$ is superlinear.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑