Abstract
Based on the eigensystem {λj,Oj} of -Δ, the multiple solutions for nonlinear problem Δu + 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) = u 3 in a square and L-shape domain are presented. The results show that there exist at least 3 k -1 distinct nonzero solutions corresponding to each k-ple eigenvalue of -Δ (Conjecture 1).
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