Based on the eigensystem {λj, φj} of -△, the multiple solutions for nonlinear problem △u + f(u)= 0 in Ω,u = 0 on Ω are approximated. A new search-extension method (SEM) is proposed, which consists of three algorithms in three level subspaces.Numerical experiments for f(u)= u3 in a square and L-shape domain are presented. The results show that there exist at least 3κ - 1 distinct nonzero solutions corresponding to each κ-ple eigenvalue of -△ (Conjecture 1).