The Properties Of Solutions For Several Integral Systems With Negative Exponents

Many researchers have studied the Lane-Emden type integral equations?system?and Wolff type integral equations?system?.But most of their results are integral equa-tions?system?with positive exponents.In this paper,we consider the Lane-Emden type integral system and Wolff type integral system with negative exponents.In this paper,we mainly consider some properties of the positive solutions of Lame-Emden type and Wolff type integral system with negative exponents,such as integrability,decay rates,symmetry etc.We use the estimates the equivalence of the positive solutions to obtian the asymptotic rates of the positive solutions,and then we have the integrability of the positive solutions.In addition,in this paper,we assume c₁?x?,c₂?x?are double bounded functions.When they are constants,the solutions of integral system involving them are radial symmetry.The paper consists of four chapter:In chapter 1,we introduce the sciential background and having obtained results of integral equations?system?,the main works in this paper and its prepare knowledge of this paper.In chapter 2,we mainly consider some properties of the positive solutions of the Lane-Emden type integral system with negative exponents;In chapter 3,according to the different forms of Wolff potentials,we discuss the properties of the positive solutions in two cases:n>??and n<??,respectively;In chapter 4,we mainly discuss the properties of the Lane-Emden type system are generalized to the general forms.