http://hdl.handle.net/20.500.12323/1766 2026-04-05T18:22:17Z http://hdl.handle.net/20.500.12323/7947 Title: The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators Authors: Allahverdiev, Bilender P.; Tuna, Hüseyin; Isayev, Hamlet A. Abstract: In this study, the resolvent of the impulsive singular Hahn–Sturm– Liouville operator is considered. An integral representation for the resolvent of this operator is obtained. 2025-03-01T00:00:00Z http://hdl.handle.net/20.500.12323/7938 Title: Eigenfunction Expansions for Singular Impulsive Dynamic Dirac Systems Authors: Allahverdiev, Bilender P.; Tuna, Hüseyin; Isayev, Hamlet A. Abstract: In this article, a spectral function for the singular impulsive dynamic Dirac system is obtained. In terms of this function, the Parseval equality and expansion formula in eigenfunctions is given. 2025-02-18T00:00:00Z http://hdl.handle.net/20.500.12323/7885 Title: Nonlinear impulsive Hahn—Sturm—Liouville problems on the whole line Authors: Allahverdiev, B. P.; Tuna, H.; Isayev, H. A. Abstract: Impulsive Hahn—Sturm—Liouville problems in singular cases are discussed. The existence of solutions of such equations on the whole axis and in the case of Weyl’s limit-circle has been investigated. First, we construct the corresponding Green’s function. This boundary-value problem is thus reduced to a fixed point problem. Later, we demonstrate the existence and uniqueness of the solutions to this problem by using the traditional Banach fixed point theorem. Finally, we derive an existence theorem without considering the solution’s uniqueness. We apply the well-known Schauder fixed point to obtain this result. 2024-01-01T00:00:00Z http://hdl.handle.net/20.500.12323/7765 Title: Impulsive q-Sturm–Liouville problems Authors: Allahverdiev, Bilender P.; Isayev, Hamlet A.; Tuna, Hüseyin Abstract: In this study, impulsive q-Sturm–Liouville problems are considered. First, symmetry is obtained with the help of boundary conditions. Then, the existence and uniqueness problem for such equations is discussed. Finally, eigenfunction expansion was obtained with the help of characteristic determinant and Green’s function. 2024-01-01T00:00:00Z