Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2013-06-01

Journal: SCIENCE CHINA-MATHEMATICS

Included Journals: SCIE

Volume: 56

Issue: 6

Page Number: 1279-1286

ISSN: 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.