HAN Liang,XIE Junhui.Existence of solutions for a class of semilinear elliptic equations with weight function in unbounded domains[J].Journal of Yanbian University,2023,(01):26-29,88.
无界区域上一类带有权函数的半线性椭圆方程解的存在性
- Title:
- Existence of solutions for a class of semilinear elliptic equations with weight function in unbounded domains
- 文章编号:
- 1004-4353(2023)01-0026-05
- 关键词:
- 无界区域; 解的存在性; 半线性椭圆方程; Sobolev - Hardy不等式; 变分法
- Keywords:
- unbounded domain; existence of solution; semilinear elliptic equation; Sobolev - Hardy inequality; variational method
- 分类号:
- O175.25
- 文献标志码:
- A
- 摘要:
- 利用Sobolev - Hardy不等式和变分法,证明了无界区域上一类带有权函数的半线性椭圆方程解的存在性,该结果将有界区域上解的存在性及全空间上解的存在性推广到了无界的外区域上.
- Abstract:
- Existence of solutions for semilinear elliptic equations involving weight functions in unbounded domains is proved by using Sobolev - Hardy inequality and variational methods, which extends the existence of solution on bounded domain and in the whole space to the unbounded outer domain.
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备注/Memo
收稿日期: 2023-01-30
基金项目: 国家自然科学基金(11761030)
第一作者: 韩亮(1997—),男,硕士研究生,研究方向为偏微分方程理论及其应用.
通信作者: 谢君辉(1984—),女(土家族),博士,副教授,研究方向为偏微分方程理论及其应用.