Study Of Solution For Nonlinear Integral Equations With Hénon Type

In this paper,we consider the integral equation where ? is bounded domain in Rn(n? 3),1<?<n and ?,?>0,(?).This thesis is composed of four chaptersIn Chapter 1,we introduce the historical background,research status of this article and the main works of this paperChapter 2 is concerned with the existence of energy maximizing positive solu-tion in subcritical case q?<g<2Chapter 3 is concerned with the asymptotic behavior of energy maximizing positive solution as (?).We also show that the energy maximizing positive solution concentrate at a point,which is located at the bound-ary as q?(q?)+.In addition,the energy maximizing positive solution is noL-radial provided that q closes to q?.Chapter 4 is concerned with the existence of energy maximizing positive solu-tion of the integral equations with critical exponent for ?>0.