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Some Existence Results of Positive Solution to Second-Order Boundary Value Problems.

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Title: Some Existence Results of Positive Solution to Second-Order Boundary Value Problems.
Authors: Shuhong Li1 mathlsh@126.com, Xiaoping Zhang2, Yongping Sun2
Source: Abstract & Applied Analysis. 2014, p1-7. 7p.
Subjects: Fixed point theory, Functional calculus, Differential equations, Monotone operators, Boundary value problems, Coincidence theory
Abstract: We study the existence of positive and monotone solution to the boundary value problem un(t) + f(t, u(t)) = 0, 0 ≤ t ≤ 1, u(0) = ξu(1), u'(1) = ηu'(0), where ξ, η ∈ (0, 1) ∪ (1, ∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O'Regan. Finally, four examples are provided to demonstrate the availability of our main results. [ABSTRACT FROM AUTHOR]
Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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An: 100533465
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  Data: We study the existence of positive and monotone solution to the boundary value problem un(t) + f(t, u(t)) = 0, 0 ≤ t ≤ 1, u(0) = ξu(1), u'(1) = ηu'(0), where ξ, η ∈ (0, 1) ∪ (1, ∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O'Regan. Finally, four examples are provided to demonstrate the availability of our main results. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Abstract & Applied Analysis is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/2014/516452
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        Text: English
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      – SubjectFull: Functional calculus
        Type: general
      – SubjectFull: Differential equations
        Type: general
      – SubjectFull: Monotone operators
        Type: general
      – SubjectFull: Boundary value problems
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      – SubjectFull: Coincidence theory
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      – TitleFull: Some Existence Results of Positive Solution to Second-Order Boundary Value Problems.
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              Text: 2014
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