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

Abstract

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.