Some Qualitative Results Of Weighted Integral Equation And System With Negative Exponents

In this paper, we investigate positive solutions for weighted integral equations and system with negative exponents. These equations come from the study of confor-mal geometry and the best functions of classical inequations.In chapter 1, We study the integral equation where n≥1, p≠0, q< 0, and the weighted function k(x) is smooth. We consider the existence and the estimates of increasing rates of the positive entire solutions in the case that k(x) is bounded and unbounded respectively.In chapter 2, we study the integral system where n≥1, a,β, s> 0 and p, q< 0. We obtain that is a necessary condition for the existence of the C1 positive entire solutions, which is also the necessary and sufficient condition for the invariant of the system and some energy functionals under the scaling transformation.