Recovering singular Sturm-Liouville differential pencils from spectral data

Abstract

Non-self-adjoint Sturm-Liouville differential operators on the half-line with a boundary condition depending polynomially on the spectral parameter are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the spectral data. For this inverse problem we prove the uniqueness theorem and provide a procedure for constructing the solution by the method of spectral mappings.Keywords Sturm-Liouville operators · Boundary conditions with the spectral parameter · Inverse spectral problems · Method of spectral mappings Mathematics Subject Classification (2000) 34A55 · 34B24 · 47E05

Determination of differential pencils from dense nodal subset in an interior subinterval

“…For instance, the evolution equations (such as the Klein-Gordon equation [11,18]) that are used to model interactions between colliding relativistic spinless particles can be reduced to the form (1.1). Another typical example is related to vibrations of mechanical systems in viscous media; see [21,24,25]. Problems of the form (1.1) have also appeared in the physical literature in the context of scattering of waves and particles (see [10,26] and the references therein).…”