Abstract
The paper is devoted to the investigation of solvability in anisotropic Sobolev spaces for new nonlinear coefficient inverse problems for third-order differential equations with multiple characteristics. The considered equations may possess coefficients that vanish or change sign, which leads to degeneration and to a change in the direction of evolution. For the inverse problems under study, existence and uniqueness theorems for regular solutions are established. Regular solutions are understood as solutions possessing all Sobolev generalized derivatives involved in the corresponding differential equation.