Search-extension method for finding multiple solutions of nonlinear problem

作     者：CHEN Chuanmiao XIE Ziqing 

作者机构：Institute of Computation Hunan Normal University Changsha 410081 China Institute of Computation Hunan Normal University Changsha 410081 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2005年第48卷第6期

页      面：721-734页

核心收录：

学科分类：07[理学] 08[工学] 0701[理学-数学] 

基　　金：This work was supported by the Special Funds of the State Major Basic Research Projects(Grant No.G1999032804) the National Natural Science Foundation of China(Grant No.10471038) 

主　　题：nonlinear problem, multiple solutions, search-extension method, conjecture. 

摘      要：Based on the eigensystem {λj,φj}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) = u3 in a square and L-shape domain are presented. The results show that there exist at least 3k - 1 distinct nonzero solutions corresponding to each κ-ple eigenvalue of -Δ (Conjecture 1).