Recovery of differential equations with nonlinear dependence on the spectral parameter

Abstract

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations.

Keywords:

• Inverse problmes
• pencils of differential operators
• wave equation

AMS:

• 34A55
• 35R30