S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation
We investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0(f(s)/s)=∞. We develop a bifurcation approach to...
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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/10.1155/2017/1069491 |
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| author | Jinxiang Wang Ruyun Ma Jin Wen |
| author_facet | Jinxiang Wang Ruyun Ma Jin Wen |
| author_sort | Jinxiang Wang |
| collection | DOAJ |
| description | We investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0(f(s)/s)=∞. We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions f[n] satisfying f[n]→f and (f[n])0→∞. By studying the auxiliary problems, we get a sequence of unbounded connected components C[n], and, then, we find an unbounded connected component C in the set of positive solutions of the fourth-order boundary value problem which satisfies 0,0∈C⊂limsupC[n] and is S-shaped. |
| format | Article |
| id | doaj-art-fee906707b094e809c3b0ed665d4f01d |
| 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-fee906707b094e809c3b0ed665d4f01d2025-02-03T01:11:12ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/10694911069491S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam EquationJinxiang Wang0Ruyun Ma1Jin Wen2Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe investigate the existence of S-shaped connected component in the set of positive solutions of the fourth-order boundary value problem: u′′′′x=λhxfux, x∈(0,1),u(0)=u(1)=u′′0=u′′1=0, where λ>0 is a parameter, h∈C[0,1], and f∈C[0,∞) with f0≔lims→0(f(s)/s)=∞. We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions f[n] satisfying f[n]→f and (f[n])0→∞. By studying the auxiliary problems, we get a sequence of unbounded connected components C[n], and, then, we find an unbounded connected component C in the set of positive solutions of the fourth-order boundary value problem which satisfies 0,0∈C⊂limsupC[n] and is S-shaped.http://dx.doi.org/10.1155/2017/1069491 |
| spellingShingle | Jinxiang Wang Ruyun Ma Jin Wen S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation Journal of Function Spaces |
| title | S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation |
| title_full | S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation |
| title_fullStr | S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation |
| title_full_unstemmed | S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation |
| title_short | S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation |
| title_sort | s shaped connected component for nonlinear fourth order problem of elastic beam equation |
| url | http://dx.doi.org/10.1155/2017/1069491 |
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