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 boundaryvalue problem of determining the lowest coefficient in one fourth order equation. The original problem is reduced toan equivalent problem. The existence and uniqueness of the integral equation are proved by means of the contractionmappings principle, and we obtained that this solution is unique for a boundary value problem. Further, using thesefacts, we prove the existence and uniqueness of the classical solution for this problem.