Structure of multiple solutions for nonlinear differential equations  

作　　者：CHEN Chuanmiao XIE Ziqing 

机构地区：[1]Institute of Computation, Hunan Normal University, Changsha 410081, China Institute of Computation, Hunan Normal University, Changsha 410081, China

出　　处：《Science China Mathematics》2004年第z1期172-180,共9页中国科学：数学（英文版）

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).

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.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), 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.

关 键 词：nonlinear problem  multiple solutions  search-extension method  structure  conjecture. 

分 类 号：N[自然科学总论]