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On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations. (English) Zbl 1224.34075
Summary: The two-point boundary value problem \[ u'' + h(x) u^p = 0, \; a < x < b, \; u(a) = u(b) = 0 \] is considered, where \(p>1\), \(h \in C^1[0,1]\) and \(h(x)>0\) for \(a \leq x \leq b\). The existence of positive solutions is well-known. Several sufficient conditions have been obtained for the uniqueness of positive solutions. On the other hand, a non-uniqueness example was given by R. A. Moore and Z. Nehari [Trans. Am. Math. Soc. 93, 30–52 (1959; Zbl 0089.06902)]. In this paper, new uniqueness results are presented.

MSC:
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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