An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction
We discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. Under a condition allowing that f(t,u,v) is superlinear in u...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/694590 |
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| _version_ | 1832553021131718656 |
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| author | Yongxiang Li He Yang |
| author_facet | Yongxiang Li He Yang |
| author_sort | Yongxiang Li |
| collection | DOAJ |
| description | We discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. Under a condition allowing that f(t,u,v) is superlinear in u and v, we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem. |
| format | Article |
| id | doaj-art-e71a11520dbf4b1f83862341b0c8ba75 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e71a11520dbf4b1f83862341b0c8ba752025-02-03T05:57:11ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/694590694590An Existence and Uniqueness Result for a Bending Beam Equation without Growth RestrictionYongxiang Li0He Yang1Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe discuss the solvability of the fourth-order boundary value problem u(4)=f(t,u,u′′), 0≤t≤1, u(0)=u(1)=u′′(0)=u′′(1)=0, which models a statically bending elastic beam whose two ends are simply supported, where f:[0,1]×R2→R is continuous. Under a condition allowing that f(t,u,v) is superlinear in u and v, we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.http://dx.doi.org/10.1155/2010/694590 |
| spellingShingle | Yongxiang Li He Yang An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction Abstract and Applied Analysis |
| title | An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction |
| title_full | An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction |
| title_fullStr | An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction |
| title_full_unstemmed | An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction |
| title_short | An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction |
| title_sort | existence and uniqueness result for a bending beam equation without growth restriction |
| url | http://dx.doi.org/10.1155/2010/694590 |
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