Eigenfunction expansion method for multiple solutions of semilinear elliptic equations with polynomial nonlinearity (Q2870623)
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scientific article; zbMATH DE number 6248276
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Eigenfunction expansion method for multiple solutions of semilinear elliptic equations with polynomial nonlinearity |
scientific article; zbMATH DE number 6248276 |
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21 January 2014
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semilinear elliptic equation
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eigenfunction expansion discretization
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error analysis
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polynomial system
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homotopy continuation
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spurious solution
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Eigenfunction expansion method for multiple solutions of semilinear elliptic equations with polynomial nonlinearity (English)
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The paper studies eigenfunction expansion discretization for finding multiple solutions of semilinear elliptic equations with polynomial nonlinearity. Error estimates of the discretization are derived. An efficient polynomial homotopy is constructed for computing all solutions of the resulting polynomial system on coarse level. Numerical results are provided to verify the error estimates derived, the efficiency of the homotopy, and the effectiveness of the filter strategy. A specific case of the Lazer-McKenna conjecture is numerically verified.
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