| Based on the Search-Extend-Method (SEM) that proposed by C.M.Chen and Z.Q.Xie for computing multiple solutions of nonlinear elliptic equation, the Expand-Subspace-Technique (EST) is supplied to optimize the rough initial value to ensure computational convergence, and the Morse theory is introduced into the SEM to explore the property of the solution meaningfully.Main results follows:(1) EST optimize the rough initial value to avoid iteration divergence which is caused by its bad approximation to the solution, through which we can verifies the assumption about the structure and distribution of the multiple solutions of odd nonlinear equations in numerical sense, and obtain the corresponding ' solution from any given initial guess .(2) Further, through changing the Morse index of the infinite dimensional solution into the finite dimensional one ,we find that the high frequence solution has large Morse index and then establish some preliminary relations between Morse index and the solution. |
