Abstract
We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for −Δu = u 3, 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.
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Zhang, X., Yu, B. & Zhang, J. Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity. Sci. China Math. 56, 1279–1286 (2013). https://doi.org/10.1007/s11425-012-4555-z
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DOI: https://doi.org/10.1007/s11425-012-4555-z