一类奇异半线性椭圆方程解的不存在性

周文书, 魏晓丹, 秦绪龙

数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 125-130.

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数学学报 ›› 2014, Vol. 57 ›› Issue (1) : 125-130. DOI: 10.12386/A2014sxxb0012
论文

一类奇异半线性椭圆方程解的不存在性

    周文书1, 魏晓丹1, 秦绪龙2
作者信息 +

Nonexistence of Solutions for a Singular Semilinear Elliptic Equation

    Wen Shu ZHOU1, Xiao Dan WEI1, Xu Long QIN2
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文章历史 +

摘要

研究了一类奇异半线性椭圆方程解的不存在性,改进并补充了Arcoya等人的一个研究工作[Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042].本文使用的方法非常简单, 证明过程中用到了Poincaré不等式,Lusin定理以及Egoroff定理.

Abstract

We study the nonexistence of solutions for a singular semilinear elliptic equations. The results improve and implement a work by Arcoya et al. [Existence and nonexistence of solutions for singular quadratic quasilinear equations, J. Differential Equations, 2009, 246: 4006-4042], whose proofs are very simple and based on Poincaré inequality, Lusin theorem and Egoroff theorem.

关键词

奇异椭圆方程 / 不存在性 / 逼近问题

Key words

singular elliptic equation / nonexistence / approximation problem

引用本文

导出引用
周文书, 魏晓丹, 秦绪龙. 一类奇异半线性椭圆方程解的不存在性. 数学学报, 2014, 57(1): 125-130 https://doi.org/10.12386/A2014sxxb0012
Wen Shu ZHOU, Xiao Dan WEI, Xu Long QIN. Nonexistence of Solutions for a Singular Semilinear Elliptic Equation. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 125-130 https://doi.org/10.12386/A2014sxxb0012

参考文献

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基金

国家自然科学基金项目(10901030,11001278);中国博士后科研基金项目(20090450191);中央高校基本科研业务费专项基金项目(DC110109,DC120101064)
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