Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions
We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, a...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/7308025 |
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| _version_ | 1832553245634985984 |
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| author | Dongliang Yan |
| author_facet | Dongliang Yan |
| author_sort | Dongliang Yan |
| collection | DOAJ |
| description | We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h: [0, 1] ⟶ [0, ∞) is continuous. Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space. |
| format | Article |
| id | doaj-art-231de0f953e34c40af326d84c8fb8ea3 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-231de0f953e34c40af326d84c8fb8ea32025-02-03T05:54:26ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/73080257308025Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary ConditionsDongliang Yan0Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaWe show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h: [0, 1] ⟶ [0, ∞) is continuous. Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.http://dx.doi.org/10.1155/2020/7308025 |
| spellingShingle | Dongliang Yan Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions Journal of Function Spaces |
| title | Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions |
| title_full | Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions |
| title_fullStr | Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions |
| title_full_unstemmed | Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions |
| title_short | Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions |
| title_sort | positive solutions for a singular superlinear fourth order equation with nonlinear boundary conditions |
| url | http://dx.doi.org/10.1155/2020/7308025 |
| work_keys_str_mv | AT dongliangyan positivesolutionsforasingularsuperlinearfourthorderequationwithnonlinearboundaryconditions |