Eigenvalues and symmetric positive solutions for a three-point boundary-value problem
In this paper, we consider the second-order three-point boundary-value problem $$displaylines{ u''(t)+f(t,u,u',u'')=0,quad 0leq tleq 1,cr u(0)=u(1)=alpha u(eta). }$$ Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least...
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| Format: | Article |
| Language: | English |
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Texas State University
2005-11-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2005/127/abstr.html |
| _version_ | 1818981550891466752 |
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| author | Yongping Sun |
| author_facet | Yongping Sun |
| author_sort | Yongping Sun |
| collection | DOAJ |
| description | In this paper, we consider the second-order three-point boundary-value problem $$displaylines{ u''(t)+f(t,u,u',u'')=0,quad 0leq tleq 1,cr u(0)=u(1)=alpha u(eta). }$$ Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem. |
| first_indexed | 2024-12-20T17:33:07Z |
| format | Article |
| id | doaj.art-1f867682ac18447e8e46e72fbe32e0f0 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T17:33:07Z |
| publishDate | 2005-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1f867682ac18447e8e46e72fbe32e0f02022-12-21T19:31:19ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-11-01200512717Eigenvalues and symmetric positive solutions for a three-point boundary-value problemYongping SunIn this paper, we consider the second-order three-point boundary-value problem $$displaylines{ u''(t)+f(t,u,u',u'')=0,quad 0leq tleq 1,cr u(0)=u(1)=alpha u(eta). }$$ Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem.http://ejde.math.txstate.edu/Volumes/2005/127/abstr.htmlSymmetric positive solutionthree-point boundary-value problemSchauder fixed point theoremeigenvalue. |
| spellingShingle | Yongping Sun Eigenvalues and symmetric positive solutions for a three-point boundary-value problem Electronic Journal of Differential Equations Symmetric positive solution three-point boundary-value problem Schauder fixed point theorem eigenvalue. |
| title | Eigenvalues and symmetric positive solutions for a three-point boundary-value problem |
| title_full | Eigenvalues and symmetric positive solutions for a three-point boundary-value problem |
| title_fullStr | Eigenvalues and symmetric positive solutions for a three-point boundary-value problem |
| title_full_unstemmed | Eigenvalues and symmetric positive solutions for a three-point boundary-value problem |
| title_short | Eigenvalues and symmetric positive solutions for a three-point boundary-value problem |
| title_sort | eigenvalues and symmetric positive solutions for a three point boundary value problem |
| topic | Symmetric positive solution three-point boundary-value problem Schauder fixed point theorem eigenvalue. |
| url | http://ejde.math.txstate.edu/Volumes/2005/127/abstr.html |
| work_keys_str_mv | AT yongpingsun eigenvaluesandsymmetricpositivesolutionsforathreepointboundaryvalueproblem |