A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

doi:10.1007/s10473-019-0121-x

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 284-296.doi: 10.1007/s10473-019-0121-x

A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

许建开¹, 谭忠², 王伟伟³, 熊泽鹏⁴

1. College of Sciences;College of Computer Science, Hunan Agriculture University, Changsha 410128, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 361000, China;
4. The First Middle School of Longhui, Longhui 422200, China

收稿日期:2017-03-08 修回日期:2018-06-06 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Jiankai XU E-mail:jiankaixu@126.com
作者简介:Zhong TAN,ztan85@163.com;Weiwei WANG, wei.wei.84@163.com;Zepeng XIONG,770685723@qq.com
基金资助:
Supported by National Natural Science Foundation of China (11126148, 11501116, 11671086, 11871208), Natural Science Foundation of Hunan Province of China (2018JJ2159), the Project Supported by Scientific Research Fund of Hunan Provincial Education Department (16C0763) and the Education Department of Fujian Province (JA15063).

A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

Jiankai XU¹, Zhong TAN², Weiwei WANG³, Zepeng XIONG⁴

1. College of Sciences;College of Computer Science, Hunan Agriculture University, Changsha 410128, China;
2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 361000, China;
4. The First Middle School of Longhui, Longhui 422200, China

Received:2017-03-08 Revised:2018-06-06 Online:2019-02-25 Published:2019-03-13
Contact: Jiankai XU E-mail:jiankaixu@126.com
Supported by:
Supported by National Natural Science Foundation of China (11126148, 11501116, 11671086, 11871208), Natural Science Foundation of Hunan Province of China (2018JJ2159), the Project Supported by Scientific Research Fund of Hunan Provincial Education Department (16C0763) and the Education Department of Fujian Province (JA15063).

摘要/Abstract

摘要： This paper is devoted to studying the existence of positive solutions for the following integral system

It is shown that if (u, v) is a pair of positive Lebesgue measurable solutions of this integral system, then
1/p-1+1/q-1=λ/n,
which is different from the well-known case of the Lane-Emden system and its natural extension, the Hardy-Littlewood-Sobolev type integral equations.

关键词: integral equations, Lane-Emden system, conformal invariance, positive solutions, existence

Abstract: This paper is devoted to studying the existence of positive solutions for the following integral system

It is shown that if (u, v) is a pair of positive Lebesgue measurable solutions of this integral system, then
1/p-1+1/q-1=λ/n,
which is different from the well-known case of the Lane-Emden system and its natural extension, the Hardy-Littlewood-Sobolev type integral equations.

Key words: integral equations, Lane-Emden system, conformal invariance, positive solutions, existence

许建开, 谭忠, 王伟伟, 熊泽鹏. A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS[J]. 数学物理学报(英文版), 2019, 39(1): 284-296.

Jiankai XU, Zhong TAN, Weiwei WANG, Zepeng XIONG. A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS[J]. Acta mathematica scientia,Series B, 2019, 39(1): 284-296.

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A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

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