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Zbl 1222.34027
Caballero, J.; Harjani, J.; Sadarangani, K.
Uniqueness of positive solutions for a class of fourth-order boundary value problems. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 543035, 13 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: $$y^{(4)}(t) = f(t, y(t)),\quad t \in [0 ,1],\quad y(0) = y(1) = y'(0) = y'(1) = 0.$$ Moreover, under certain assumptions, we prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and compare our results with the ones obtained in recent papers. Our analysis relies on a fixed-point theorem in partially ordered metric spaces.

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
47N20 Appl. of operator theory to differential and integral equations

Keywords: symmetric positive solution; fixed-point theorem

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