Geodesic
On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations
Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 189-198
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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.
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.
DOI : 10.21136/MB.2010.140696
Classification : 34B15
Keywords: uniqueness; positive solution; two-point boundary value problem; Emden-Fowler equation 
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Tanaka, Satoshi. On the uniqueness of positive solutions for two-point boundary value problems of Emden-Fowler differential equations. Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 189-198. doi: 10.21136/MB.2010.140696

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