Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems
The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: 𝑦(4)(𝑡)=𝑓(𝑡,𝑦(𝑡)), 𝑡∈[0,1], 𝑦(0)=𝑦(1)=𝑦(0)=𝑦(1)=0. Moreover, under certain assumptions, we will prove that the above boundary value problem has a un...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/543035 |
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| Summary: | The purpose of this paper is to investigate the existence and uniqueness of
positive solutions for the following fourth-order boundary value problem: 𝑦(4)(𝑡)=𝑓(𝑡,𝑦(𝑡)), 𝑡∈[0,1], 𝑦(0)=𝑦(1)=𝑦(0)=𝑦(1)=0. Moreover, under certain assumptions, we will prove that the above boundary
value problem has a unique symmetric positive solution.
Finally, we present some examples and we compare our results with the ones
obtained in recent papers.
Our analysis relies on a fixed point theorem in partially ordered metric spaces. |
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| ISSN: | 1085-3375 1687-0409 |