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Satoshi Tanaka, Department of Applied Mathematics, Faculty of Science, Okayama University of Science, Ridaichou 1-1, Okayama 700-0005, Japan, e-mail: tanaka@xmath.ous.ac.jp
Abstract: The two-point boundary value problem
u" + h(x) u^p = 0, \quad a < x < b, \qquad u(a) = u(b) = 0
is considered, where $p>1$, $h \in C^1[0,1]$ and $h(x)>0$ for $a \le x \le b$. 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 Moore and Nehari in 1959. In this paper, new uniqueness results are presented.
Keywords: uniqueness, positive solution, two-point boundary value problem, Emden-Fowler equation
Classification (MSC 2010): 34B15
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