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Uniqueness of positive solutions of nonlinear second-order equations

Author: Robert Dalmasso
Journal: Proc. Amer. Math. Soc. 123 (1995), 3417-3424
MSC: Primary 34B15; Secondary 34A12
MathSciNet review: 1301018
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Abstract: In this paper we study the uniqueness question of positive solutions of the two-point boundary value problem: $ u''(t) + f(\vert t\vert,u(t)) = 0, - R < t < R,u( \pm R) = 0$ where $ R > 0$ is fixed and $ f:[0,R] \times [0,\infty ) \to \mathbb{R}$ is in $ {C^1}([0,R] \times [0,\infty ))$. A uniqueness result is proved when f satisfies some appropriate conditions. Some examples illustrating our theorem are also given.

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Keywords: Two-point boundary value problem, positive solutions, uniqueness
Article copyright: © Copyright 1995 American Mathematical Society

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