Antibound States and Exponentially Decaying Sturm-Liouville Potentials

We consider the Sturm–Liouville equation y'(x)+{–q(x)}y(x)=0 (0x<) (1.1) with a boundary condition at x = 0 which can be either the Dirichletcondition y(0)=0 (1.2) or the Neumann condition y'(0)=0 (1.3) As usual, is the complex spectral parameter with 0 arg <2, and the potential q is real-valued and locally integrablein [0, ).