On solvability of inverse problem for one equation of fourth order

Abstract

The work is devoted to study the existence and uniqueness of the classical solution of the inverse boundary value problem of determining the lowest coefficient in one fourth order equation. The original problem is reduced to an equivalent problem. The existence and uniqueness of the integral equation are proved by means of the contraction mappings principle, and we obtained that this solution is unique for a boundary value problem. Further, using these facts, we prove the existence and uniqueness of the classical solution for this problem.