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Zbl 1237.34153
Goodrich, Christopher S.
Positive solutions to boundary value problems with nonlinear boundary conditions.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 417-432 (2012). ISSN 0362-546X

The author considers the boundary value problem $$y^{\Delta\Delta}=-\lambda f(t,y^\sigma(t)),$$ subject to the boundary conditions $$y(a)=\phi(y) \text{ and }y(\sigma^2(b))=0.$$ They give the form of solutions of the boundary value problem, and apply cone theoretic tools to prove that the problem has at least one positive solution. At the end of this paper, some examples are worked out to illustrate the main results.
[Zhenlai Han (Jinan)]
MSC 2000:
*34N05
34B09 Boundary value problems with an indefinite weight
34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems

Keywords: time scales; second-order boundary value problem; nonlocal boundary condition; cone; positive solution

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