Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations
Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: u(4)=f(t,u(t)), t∈[0,1]; u(0)=u(1)=u′′(0)=u′′(1)=0, where f∈C([0,1]×ℝ1,ℝ1). In particular, an infinitely many sign changing solution theorem is established....
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/635265 |
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| _version_ | 1832560599034232832 |
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| author | Ying Wu Guodong Han |
| author_facet | Ying Wu Guodong Han |
| author_sort | Ying Wu |
| collection | DOAJ |
| description | Several new existence theorems on positive, negative, and sign-changing
solutions for the following fourth-order beam equation are obtained: u(4)=f(t,u(t)), t∈[0,1]; u(0)=u(1)=u′′(0)=u′′(1)=0, where f∈C([0,1]×ℝ1,ℝ1). In particular, an infinitely many sign changing solution
theorem is established. The method of the invariant set of decreasing
flow is employed to discuss this problem. |
| format | Article |
| id | doaj-art-5ccd5f2315b64789834651b021bf1228 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5ccd5f2315b64789834651b021bf12282025-02-03T01:27:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/635265635265Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam EquationsYing Wu0Guodong Han1College of Science, Xi’an University of Science and Technology, Xi’an, Shaanxi 710054, ChinaCollege of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062, ChinaSeveral new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: u(4)=f(t,u(t)), t∈[0,1]; u(0)=u(1)=u′′(0)=u′′(1)=0, where f∈C([0,1]×ℝ1,ℝ1). In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem.http://dx.doi.org/10.1155/2013/635265 |
| spellingShingle | Ying Wu Guodong Han Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations Abstract and Applied Analysis |
| title | Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations |
| title_full | Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations |
| title_fullStr | Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations |
| title_full_unstemmed | Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations |
| title_short | Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations |
| title_sort | infinitely many sign changing solutions for some nonlinear fourth order beam equations |
| url | http://dx.doi.org/10.1155/2013/635265 |
| work_keys_str_mv | AT yingwu infinitelymanysignchangingsolutionsforsomenonlinearfourthorderbeamequations AT guodonghan infinitelymanysignchangingsolutionsforsomenonlinearfourthorderbeamequations |