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Uniqueness of positive solutions
for Sturm-Liouville boundary value problems

Author: Fu-Hsiang Wong
Journal: Proc. Amer. Math. Soc. 126 (1998), 365-374
MSC (1991): Primary 34B15; Secondary 35J25, 35J65, 47H15
MathSciNet review: 1443860
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Abstract: Sufficient conditions for the uniqueness of positive solutions of singular Sturm-Liouville boundary value problems

\begin{equation*}\begin{cases} (\mathrm E)\ (|u'|^{m-2}u')'+f(t,u,u')=0,\quad\text{in}\ (\theta _1,\theta _2),m\ge 2,\\ (\mathrm{BC})\begin{cases} \alpha _1u(\theta _1)-\beta _1u'(\theta _1)=0,\\ \alpha _2u(\theta _2)+\beta _2u'(\theta _2)=0, \end{cases} \end{cases} \tag{BVP} \end{equation*}

where $\alpha _i,\beta _i\ge 0$ and $\alpha _i^2+\beta _i^2\not=0$ $(i=1,2)$, are established.

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Additional Information

Fu-Hsiang Wong
Affiliation: Department of Mathematics and Science, National Taipei Teacher’s College, 134, Ho-Ping e. Rd. Sec. 2, Taipei 10659, Taiwan, Republic of China

Keywords: Sturm-Liouville BVPs, positive solution, singular and uniqueness.
Received by editor(s): April 17, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society

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