Indexed by:期刊论文

Date of Publication:2013-06-01

Journal:SCIENCE CHINA-MATHEMATICS

Included Journals:SCIE

Volume:56

Issue:6

Page Number:1279-1286

ISSN No.:1674-7283

Key Words:elliptic equation; cubic nonlinearity; multiplicity of eigenvalue

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