Articles

A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

  • Jiankai XU ,
  • Zhong TAN ,
  • Weiwei WANG ,
  • Zepeng XIONG
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  • 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 date: 2017-03-08

  Revised date: 2018-06-06

  Online published: 2019-03-13

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).

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.

Cite this article

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 . DOI: 10.1007/s10473-019-0121-x

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