On homotopy continuation method for computing multiple solutions to the Henon equation Academic Article uri icon


  • Motivated by numerical examples in solving semilinear elliptic PDEs for multiple solutions, some properties of Newton homotopy continuation method, such as its continuation on symmetries, the Morse index, and certain functional structures, are established. Those results provide useful information on selecting initial points for the method to find desired solutions. As an application, a bifurcation diagram, showing the symmetry/peak breaking phenomena of the Henon equation, is constructed. 2007 Wiley Periodicals, Inc.

published proceedings

  • Numerical Methods for Partial Differential Equations

author list (cited authors)

  • Chen, X., & Zhou, J.

citation count

  • 3

complete list of authors

  • Chen, Xianjin||Zhou, Jianxin

publication date

  • May 2008