Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity  

作　　者：ZHANG XuPing YU Bo ZHANG JinTao 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology

出　　处：《Science China Mathematics》2013年第6期1279-1286,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.11171051 and 91230103)

摘　　要：We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkin- eigenfunction discretization for -△u = u^3, when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -△, the discretized problem has at least 3^N - 1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -△.

关 键 词：elliptic equation cubic nonlinearity multiplicity of eigenvalue 

分 类 号：O175.25[理学—数学] TP18[理学—基础数学]