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Erratum to: New results of positive solutions for the Sturm-Liouville problem

The original article was published in Boundary Value Problems 2016 2016:64

Unfortunately, the original version of this article [1] contained an error. At the top of page 14, $\underline{w}$ in the following expression should be replaced by ω, that is,

$$ p(t)z_{*}'(t)=\frac{\mu_{1}(L_{\psi}^{(n_{0})})}{\Gamma} \left \{ \textstyle\begin{array}{@{}l@{\quad}l} \alpha\int_{\frac{1}{n_{0}}}^{1-\frac{1}{n_{0}}} \underline{w}_{1}(s)\psi(s)z_{*}(s)\,ds \\ -\gamma\int_{\frac{1}{n_{0}}}^{t} \underline{w}_{0}(s)\psi(s)z_{*}(s)\,ds,& 0\leq t< 1/n_{0}, \\ +\alpha\int_{t}^{1-\frac{1}{n_{0}}} \underline{w}_{1}(s)\psi(s)z_{*}(s)\,ds, & 1/n_{0}\leq t\leq1-1/n_{0}, \\ -\gamma\int_{\frac{1}{n_{0}}}^{1-\frac{1}{n_{0}}} \underline{w}_{0}(s)\psi(s)z_{*}(s)\,ds, & 1-1/n_{0}< t\leq1, \end{array}\displaystyle \right . $$

should be

$$ p(t)z_{*}'(t)=\frac{\mu_{1}(L_{\psi}^{(n_{0})})}{\Gamma} \left \{ \textstyle\begin{array}{@{}l@{\quad}l} \alpha\int_{\frac{1}{n_{0}}}^{1-\frac{1}{n_{0}}} {\omega}_{1}(s)\psi(s)z_{*}(s)\,ds,& 0\leq t< 1/n_{0}, \\ -\gamma\int_{\frac{1}{n_{0}}}^{t} {\omega}_{0}(s)\psi(s)z_{*}(s)\,ds \\ \quad {}+\alpha\int_{t}^{1-\frac{1}{n_{0}}} {\omega}_{1}(s)\psi(s)z_{*}(s)\,ds, & 1/n_{0}\leq t\leq1-1/n_{0}, \\ -\gamma\int_{\frac{1}{n_{0}}}^{1-\frac{1}{n_{0}}} {\omega}_{0}(s)\psi(s)z_{*}(s)\,ds, & 1-1/n_{0}< t\leq1. \end{array}\displaystyle \right . $$

We would like to apologize for this error and for any inconvenience this may have caused.

References

  1. 1.

    Yang, GC, Feng, HB: New results of positive solutions for the Sturm-Liouville problem. Bound. Value Probl. 2016, 64 (2016). doi:10.1186/s13661-016-0571-1

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Correspondence to GC Yang.

Additional information

The online version of the original article can be found under doi:10.1186/s13661-016-0571-1.

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