On a Fourth-Order Boundary Value Problem at Resonance
We investigate the spectrum structure of the eigenvalue problem u4x=λux, x∈0,1; u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx, x∈0,1; u0=u1=u′0=u′1=0, which models a...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/2641856 |
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| _version_ | 1832564404646838272 |
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| author | Man Xu Ruyun Ma |
| author_facet | Man Xu Ruyun Ma |
| author_sort | Man Xu |
| collection | DOAJ |
| description | We investigate the spectrum structure of the eigenvalue problem u4x=λux, x∈0,1; u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx, x∈0,1; u0=u1=u′0=u′1=0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded. |
| format | Article |
| id | doaj-art-5e8589671a304b97ae6e691145886fad |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5e8589671a304b97ae6e691145886fad2025-02-03T01:11:04ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/26418562641856On a Fourth-Order Boundary Value Problem at ResonanceMan Xu0Ruyun Ma1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe investigate the spectrum structure of the eigenvalue problem u4x=λux, x∈0,1; u0=u1=u′0=u′1=0. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance -u4x+λ1ux+gx,ux=hx, x∈0,1; u0=u1=u′0=u′1=0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded.http://dx.doi.org/10.1155/2017/2641856 |
| spellingShingle | Man Xu Ruyun Ma On a Fourth-Order Boundary Value Problem at Resonance Journal of Function Spaces |
| title | On a Fourth-Order Boundary Value Problem at Resonance |
| title_full | On a Fourth-Order Boundary Value Problem at Resonance |
| title_fullStr | On a Fourth-Order Boundary Value Problem at Resonance |
| title_full_unstemmed | On a Fourth-Order Boundary Value Problem at Resonance |
| title_short | On a Fourth-Order Boundary Value Problem at Resonance |
| title_sort | on a fourth order boundary value problem at resonance |
| url | http://dx.doi.org/10.1155/2017/2641856 |
| work_keys_str_mv | AT manxu onafourthorderboundaryvalueproblematresonance AT ruyunma onafourthorderboundaryvalueproblematresonance |