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国际应用数学进展

Advances in International Applied Mathematics

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Advances in International Applied Mathematics. 2022; 4: (1) ; 10.12208/j.aam.20220001 .

Positive solutions to a class of singularelliptic systems
一类奇异椭圆方程组的正解

作者： 申亚琳 *, 冯美强

北京信息科技大学理学院 北京

*通讯作者： 申亚琳,单位：北京信息科技大学理学院 北京；

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引用本文: 申亚琳, 冯美强 一类奇异椭圆方程组的正解[J]. 国际应用数学进展, 2022; 4: (1) : 1-11.
Published: 2022/5/21 11:14:54

摘要

本文的主要目的是研究一类带奇异权函数的椭圆方程组。通过运用锥上的不动点指数定理，我们得到了该类椭圆方程组在不同参数区间内正径向解存在性、多重性和不存在性的新结果。

关键词： 奇异椭圆方程组；正径向解；存在性；多重性；不存在性；不动点指数；锥

Abstract

The goal of this paper is to study a class of elliptic systems with singular weight function. By using the fixed point index in a cone, we derive new results for the existence, nonexistence and multiplicity of positive radial solutions to this class of elliptic systems in different parameter intervals.

Key words： Singular Elliptic System;Positive Radial Solutions; Existence; Multiplicity; Nonexistence; Fixed point index; Cone

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