Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity (Q365843)
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scientific article; zbMATH DE number 6207061
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity |
scientific article; zbMATH DE number 6207061 |
Statements
Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity (English)
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9 September 2013
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The authors prove a conjecture which states that in the Galerkin-eigenfunction 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.
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elliptic equation
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cubic nonlinearity
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multiplicity of eigenvalues
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Galerkin-eigenfunction discretization
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