Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations
<p/> <p>This paper investigates the eigenvalue problem for a class of singular elastic beam equations where one end is simply supported and the other end is clamped by sliding clamps. Firstly, we establish a necessary and sufficient condition for the existence of positive solutions, then...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2011/594128 |
| _version_ | 1818982939041464320 |
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| author | Lu Huiqin |
| author_facet | Lu Huiqin |
| author_sort | Lu Huiqin |
| collection | DOAJ |
| description | <p/> <p>This paper investigates the eigenvalue problem for a class of singular elastic beam equations where one end is simply supported and the other end is clamped by sliding clamps. Firstly, we establish a necessary and sufficient condition for the existence of positive solutions, then we prove that the closure of positive solution set possesses an unbounded connected branch which bifurcates from <inline-formula> <graphic file="1687-2770-2011-594128-i1.gif"/></inline-formula> Our nonlinearity <inline-formula> <graphic file="1687-2770-2011-594128-i2.gif"/></inline-formula> may be singular at <inline-formula> <graphic file="1687-2770-2011-594128-i3.gif"/></inline-formula> and/or <inline-formula> <graphic file="1687-2770-2011-594128-i4.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-20T17:55:10Z |
| format | Article |
| id | doaj.art-a5e0a6dfd5564727b5ff0999b741a3d1 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-20T17:55:10Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-a5e0a6dfd5564727b5ff0999b741a3d12022-12-21T19:30:46ZengSpringerOpenBoundary Value Problems1687-27621687-27702011-01-0120111594128Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam EquationsLu Huiqin<p/> <p>This paper investigates the eigenvalue problem for a class of singular elastic beam equations where one end is simply supported and the other end is clamped by sliding clamps. Firstly, we establish a necessary and sufficient condition for the existence of positive solutions, then we prove that the closure of positive solution set possesses an unbounded connected branch which bifurcates from <inline-formula> <graphic file="1687-2770-2011-594128-i1.gif"/></inline-formula> Our nonlinearity <inline-formula> <graphic file="1687-2770-2011-594128-i2.gif"/></inline-formula> may be singular at <inline-formula> <graphic file="1687-2770-2011-594128-i3.gif"/></inline-formula> and/or <inline-formula> <graphic file="1687-2770-2011-594128-i4.gif"/></inline-formula>.</p>http://www.boundaryvalueproblems.com/content/2011/594128 |
| spellingShingle | Lu Huiqin Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations Boundary Value Problems |
| title | Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations |
| title_full | Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations |
| title_fullStr | Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations |
| title_full_unstemmed | Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations |
| title_short | Eigenvalue Problem and Unbounded Connected Branch of Positive Solutions to a Class of Singular Elastic Beam Equations |
| title_sort | eigenvalue problem and unbounded connected branch of positive solutions to a class of singular elastic beam equations |
| url | http://www.boundaryvalueproblems.com/content/2011/594128 |
| work_keys_str_mv | AT luhuiqin eigenvalueproblemandunboundedconnectedbranchofpositivesolutionstoaclassofsingularelasticbeamequations |