A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

doi:10.1007/s10473-019-0121-x

Abstract

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

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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