The Asymptotic Behaviour Of The Ground State Solutions For Poly Harmonic Hénon Equation

This thesis concerns the study of the asymptotic behaviour of the ground s-tate solutions for polyharmonic Henon equation in a bounded and simply connected region.Consider the following equation:#12 where Ω is a bounded and simply connected region in Rn,its boundary is smooth,α>0,m is a positive integer and n>2m(n≥3).Firstly,we show the research results about Henon equation that have been given and summarize the research conclusions in this paper.Secondly,we find a minimizing sequence of the Sobolev constant by the solution of the polyharmonic Henon equation,and then prove that the ground state solution up blows up at the farthest point from the origin in the sense of measure by the concentration compactness principle arguments.Finally,we obtain that the ground state solution up has a unique maximum point and blows up at the farthest point from the origin,which deduces that the ground state solution is non-radial.