Inverse Spectral Problem for the Third-Order Differential Equation

This paper is concerned with the inverse spectral problem for third-order differential equation distribution coefficient. The consists in recovery of expression coefficients from data two boundary value problems separated conditions. For this problem, we solve most fundamental question theory about necessary and sufficient conditions solvability. In addition, prove local solvability stability problem. Furthermore, obtain very simple self-adjoint case. main results are proved by a constructive method that reduces nonlinear to linear Banach space bounded infinite sequences. future, our can be generalized various classes higher-order operators integrable or coefficients.