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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.

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
Full Text: DOI
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