Remarks on the Periodic Conformable Sturm-Liouville Problems

Abstract

The conformable Sturm–Liouville problem (CSLP), $-x^{1-\alpha }{\left(p\left(x\right)x^{1-\alpha }{y}^{\prime }\left(x\right)\right)}^{\prime }=\left(\lambda \rho \left(x\right)-q\left(x\right)\right)y\left(x\right)$ , for $0<\alpha \le 1$ , is studied under some certain conditions on the coefficients $p$ , $\rho$ , and $q$ . According to an interesting idea proposed by P. Binding and H. Volkmer [Binding et al., 2012, Binding et al., 2013], we will derive how to reduce the periodic or antiperiodic (CSLP) to an analysis of the Prüfer angle. The eigenvalue interlacing property related to (CSLP) will be given.