Asymptotics of eigenvalues and eigenfunctions of energy-dependent Sturm--Liouville equations

Abstract

We study asymptotics of eigenvalues, eigenfunctions and norming constants of singular energy-dependent Sturm--Liouville equations with complex-valued potentials. The analysis essentially exploits the integral representation of solutions, which we derive using the connection of the problem under study and a Dirac system of a special form.