Abstract: | Abstract The multiple solutions for one-dimensional cubic nonlinear problem u″ + u3 = 0, u(0) = u(π) = 0 are computed, on the basis of the eigenpairs of , k = 1, 2, 3 · · ·. There exist two nonzero solutions ±u k corresponding to each k, and their Morse index MI(k) for 1 ≤ k ≤ 20 is to be exactly determined. It is shown by the numerical results that MI(k) ≥ k. Supported by The Special Funds of State Major Basic Research Projects (No.G1999032804), National Natural Science Foundation of China (No.19331021) and Mathematical Tianyuan Youth Foundation of National Natural Science Foundation of China (No.10226016). |