Bifurcation method for computing the multiple positive solutions to p-Henon equation

Abstract

In this paper, we proposed the algorithms to solving the D4 symmetric positive solutions to the boundary value problem of p-Henon equation. Taking r in p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the D4 symmetric positive solutions is found via the extended systems. Based on the Liapunov–Schmidt reduction, other symmetric positive solutions are computed by the branch switching method.