A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation
We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/302942 |
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| author | Ping Liu Yuwen Wang |
| author_facet | Ping Liu Yuwen Wang |
| author_sort | Ping Liu |
| collection | DOAJ |
| description | We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem. |
| format | Article |
| id | doaj-art-53caadc1a21043cfa18e397faeb3517a |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-53caadc1a21043cfa18e397faeb3517a2025-08-20T02:05:24ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/302942302942A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear EquationPing Liu0Yuwen Wang1Y.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, ChinaY.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, ChinaWe consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.http://dx.doi.org/10.1155/2011/302942 |
| spellingShingle | Ping Liu Yuwen Wang A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation Abstract and Applied Analysis |
| title | A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation |
| title_full | A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation |
| title_fullStr | A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation |
| title_full_unstemmed | A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation |
| title_short | A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation |
| title_sort | fold bifurcation theorem of degenerate solutions in a perturbed nonlinear equation |
| url | http://dx.doi.org/10.1155/2011/302942 |
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