Open Access

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

Boundary Value Problems20162016:72

https://doi.org/10.1186/s13661-016-0579-6

Received: 21 March 2016

Accepted: 21 March 2016

Published: 29 March 2016

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.

Notes

Declarations

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
College of Applied Mathematics, Chengdu University of Information Technology

References

  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 View ArticleGoogle Scholar

Copyright

© Yang and Feng 2016