带有Rellich位势的临界双调和方程解的存在性

doi:10.6040/j.issn.1671-9352.0.2020.542

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (6): 42-46.doi: 10.6040/j.issn.1671-9352.0.2020.542

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带有Rellich位势的临界双调和方程解的存在性

姜瑞廷¹,翟成波^2*

1.山西财经大学应用数学学院, 山西太原 030006;2.山西大学数学科学学院, 山西太原 030006

发布日期:2021-06-03
作者简介:姜瑞廷(1990— ), 女, 博士, 讲师, 研究方向为非线性分析及其应用. E-mail:rtjiang@sxufe.edu.cn*通信作者简介:翟成波(1977— ), 男, 教授, 研究方向为非线性分析与微分方程. E-mail:cbzhai@sxu.edu.cn
基金资助:
山西省高等学校科技创新项目资助项目(2020L0260);山西财经大学青年基金资助项目(QN-202020)

Existence of solution for the critical biharmonic equations involving Rellich potentials

JIANG Rui-ting¹, ZHAI Cheng-bo^2*

1. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China;
2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China

Published:2021-06-03

摘要/Abstract

摘要： 考虑一类带有Rellich位势的临界双调和方程Δ2u-μu/(|x|4)=(|u|2^*(s)-2u)/(|x|^s)+λf(x,u),运用山路引理得到非平凡解的存在性。

关键词: Rellich 位势, Rellich-Sobolev临界指数, 局部Palais-Smale条件, 山路引理

Abstract: This paper considers a class of critical biharmonic equations involving Rellich potentials Δ²u-μu/(|x|4)=(|u|2^*(s)-2u)/(|x|^s)+λf(x,u)in a bounded domain. By mountain pass theorem, the existence of at least a nontrivial solution is obtained.

Key words: Rellich potential, Rellich-Sobolev critical exponent, local Palais-Smale condition, mountain pass theorem

中图分类号:

O175.25

姜瑞廷,翟成波. 带有Rellich位势的临界双调和方程解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(6): 42-46.

JIANG Rui-ting, ZHAI Cheng-bo. Existence of solution for the critical biharmonic equations involving Rellich potentials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(6): 42-46.

参考文献

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[4] KANG Dongsheng, XU Liangshun. Asymptotic behavior and existence results for the biharmonic problems involving Rellich potentials[J]. Journal of Mathematical Analysis and Applications, 2017, 455(2):1365-1382.
[5] 郭玉霞, 唐仲伟, 汪路顺. 带深井位势双调和方程的解[J]. 中国科学:数学, 2019, 49(1):21-38. GUO Yuxia, TANG Zhongwei, WANG Lushun. Solutions of biharmonic equations with steep potential wells[J]. Scientia Sinica Mathematics, 2019, 49(1):21-38.
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带有Rellich位势的临界双调和方程解的存在性

Existence of solution for the critical biharmonic equations involving Rellich potentials

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