Spectral Analysis for the Almost Periodic Sturm – Liouville operator with Impulse

This paper focuses on the impulsive Sturm-Liouville operator on the whole axis with complex almost periodic potentials and the discontinuous coefficient on the right-hand side.We study the most important characteristics of the fundamental solutions of the Sturm-Liouville equation.Using the impulsive condition, we determine the transfer matrix.Further, using the impulsive condition and transfer matrix, we construct Green's function and obtain the resolvent of the impulsive Sturm-Liouville operator.Also, we investigate the eigenvalues of the impulsive Sturm-Liouville operator.