Structure of multiple solutions for nonlinear differential equations |
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Authors: | Chuanmiao Chen Ziqing Xie |
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Institution: | 1.Institute of Computation,Hunan Normal University,Changsha,China |
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Abstract: | 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) = u 3, u 2, (u - p), u 2(u 2 - p), are completed and some conjectures are presented. |
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