报告题目：Classification of solutions on certain integral equations with negative exponents

报告人：湖南农业大学理学院   许建开副教授

报告时间：7月1日晚上18:30-19:30

报告地点：数计学院4号楼302室

摘要In this paper, we consider an integral system with negative exponents which is closely related to the conformally geometry. we give the sharp criteria on the existence of positive solutions and show that if $(u,v)$ is a pair of positive Lebesgue measurable solutions of the integral system, then $(p,q)$ lies on the Sobolev hyperbola curves, namely $$\\frac{1}{p-1}+\\frac{1}{q-1}=\\frac{\\lambda}{n},$$ which is distinct from the classification of well-known Lane-Emden system and its natural extension to Hardy-Littlewood-Sobolev type integral equations. Moreover, we also obtain the explicit form of positive solutions for the integral system in the case: $p=q=1+2n/\\lambda$

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