GREEN’S FUNCTION OF AN IMPULSIVE STURM – LIOUVILLE OPERATOR

Summary: This work is dedicated to the impulsive Sturm - Liouville operator on the whole axis with complex almost periodic potentials and the discontinuous coefficient on the right – hand side. We investigated the main characteristics of the fundamental solutions of the Sturm – Liouville equation. From the impulsive condition we found the transfer matrix. Using the impulsive condition and transfer matrix, we constructed Green’s function and obtained the resolvent of the impulsive Sturm – Liouville operator. In future works, eigenvalues of the impulsive Sturm - Liouville operator will be investigated. The inverse problem will be formulated, a constructive procedure for the solution of the inverse problem will be provided.