Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems
We are concerned with the following superlinear fourth-order equation u4t+utφt,−ut=0, t∈0, 1; −u0=u1=0, −u′0=a, − u′1=-b, where a,−b are nonnegative constants such that a+b>0 and φt,−s is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/384958 |
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| Summary: | We are concerned with the following superlinear fourth-order equation u4t+utφt,−ut=0, t∈0, 1; −u0=u1=0, −u′0=a, − u′1=-b, where a,−b are nonnegative constants such that a+b>0 and φt,−s is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class K satisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments. |
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| ISSN: | 2314-8896 2314-8888 |