Uniqueness of positive solutions for Sturm-Liouville boundary value problems

Wong, Fu-Hsiang

doi:10.1090/S0002-9939-98-04264-6

Uniqueness of positive solutions for Sturm-Liouville boundary value problems
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Proc. Amer. Math. Soc. 126 (1998), 365-374 Request permission

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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