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Uniqueness of positive solutions for a class of fourth-order boundary value problems. (English) Zbl 1222.34027
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:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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