Study Of Solution For Nonlinear Integral Equations With Hénon Type

In this paper,we consider the integral equation where Ω is bounded domain in Rn(n≥ 3),1<γ<n and α,β>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 qγ<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→(qγ)+.In addition,the energy maximizing positive solution is noL-radial provided that q closes to qγ.Chapter 4 is concerned with the existence of energy maximizing positive solu-tion of the integral equations with critical exponent for λ>0.