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.
Inverse boundary value problem, fourth order equation, Fourier method, classical solution
QIZI, AYSEL RAMAZANOVA TELMAN and OGLU, YASHAR MEHRELIYEV TOPUSH
"On solvability of inverse problem for one equation of fourth order,"
Turkish Journal of Mathematics: Vol. 44:
2, Article 19.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss2/19