Continuous dependence of eigenvalues on potential functions for nonlocal Sturm-Liouville equations

In this paper, we discuss the continuous dependence of eigenvalues on the potential function for a nonlocal Sturm-Liouville equation with truncated Marchaud fractional derivative term by two-parameter method. To this end, we first study the properties of eigenvalues for a two-parameter nonlocal Sturm-Liouville eigenvalue problem. We obtain the two-parameter nonlocal Sturm-Liouville eigenvalue problem that has countable number of simple real eigenvalues. Meanwhile, the asymptotic behavior of eigenvalues is studied by aid of the analytic perturbation theory.