Bifurcation Method For Computing Boundary Value Problem Of Henon Equation On The Disk Of Plane

In this dissertation, we compute and visualize multiple solutions of the boundary valueproblem of the Henon equation on the disk of planewhereΩis a unit circle, (?)Ωis the boundary ofΩ, r = (x² + y²)^1/2,l≥0,p≥1/2 which is calledpolytropic exponent in astrophysics.Using the Liapunov-Schimdt method and symmetry-breaking bifurcation theory, we computedifferent symmetry solutions of problem(0-1), especially the positive solutions with different sym-metry.The bifurcation method has two kind of advantage. Firstly, it can be used to compute the so-lutions with different symmetry as many as possible; Secondly, it can simplify the computationdue to the symmetry.