Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions
We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u(4)(t)=f(t,u(t),u′′(t)), t∈(0,1), u(0)=∫01g(s)u(s)ds, u(1)=0, u′′(0)=∫01h(s)u&...
| Main Authors: | , |
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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://dx.doi.org/10.1155/2011/297578 |
| _version_ | 1818346140826861568 |
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| author | Ruyun Ma Tianlan Chen |
| author_facet | Ruyun Ma Tianlan Chen |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | We study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u(4)(t)=f(t,u(t),u′′(t)), t∈(0,1), u(0)=∫01g(s)u(s)ds, u(1)=0, u′′(0)=∫01h(s)u′′(s)ds, u′′(1)=0, where f:[0,1]×[0,+∞)×(-∞,0]→[0,+∞) is continuous, g,h∈L1[0,1] are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques. |
| first_indexed | 2024-12-13T17:13:32Z |
| format | Article |
| id | doaj.art-73000e7e49894de582c853f4258c7ea9 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T17:13:32Z |
| publishDate | 2011-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-73000e7e49894de582c853f4258c7ea92022-12-21T23:37:30ZengSpringerOpenBoundary Value Problems1687-27621687-27702011-01-01201110.1155/2011/297578Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary ConditionsRuyun MaTianlan ChenWe study the existence of positive solutions of the following fourth-order boundary value problem with integral boundary conditions, u(4)(t)=f(t,u(t),u′′(t)), t∈(0,1), u(0)=∫01g(s)u(s)ds, u(1)=0, u′′(0)=∫01h(s)u′′(s)ds, u′′(1)=0, where f:[0,1]×[0,+∞)×(-∞,0]→[0,+∞) is continuous, g,h∈L1[0,1] are nonnegative. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques.http://dx.doi.org/10.1155/2011/297578 |
| spellingShingle | Ruyun Ma Tianlan Chen Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions Boundary Value Problems |
| title | Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions |
| title_full | Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions |
| title_fullStr | Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions |
| title_full_unstemmed | Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions |
| title_short | Existence of Positive Solutions of Fourth-Order Problems with Integral Boundary Conditions |
| title_sort | existence of positive solutions of fourth order problems with integral boundary conditions |
| url | http://dx.doi.org/10.1155/2011/297578 |
| work_keys_str_mv | AT ruyunma existenceofpositivesolutionsoffourthorderproblemswithintegralboundaryconditions AT tianlanchen existenceofpositivesolutionsoffourthorderproblemswithintegralboundaryconditions |