Structure of multiple solutions for nonlinear differential equations

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：2004年第47卷第z1期

页      面：172-180页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：This work was supported by the Special Funds of State Major Basic Research Projects(Grant No.G1999032804) the National Natural Science Foundation of China(Grant No.19871027) Mathematical Tianyuan Youth Foundation of the National Natural Science Foundation of China(No.10226016) 

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

摘      要：Based on the eigensystem {λj,φjof -Δ, the multiple solutions for nonlinear problem Δu+f(u)=0 in Ω,u=0 onαΩ are approximated. A new search-extension method (SEM), which consists of three steps in three level subspaces, is proposed. Numerical simulations for several typical nonlinear cases, i.e. f(u)=u3,u2(u-p),u2(u2-p), are completed and some conjectures are presented.