Bifurcation method for solving multiple positive solutions to boundary value problem of p-Henon equation on the unit disk

Abstract

In this paper, an algorithm is proposed to solve the O(2) symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking l in the p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2) symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.