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. |
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| 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] |
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| Database: | Engineering Source |
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