http://hdl.handle.net/20.500.12323/1766 Sun, 05 Apr 2026 18:20:22 GMT 2026-04-05T18:20:22Z 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. Sat, 01 Mar 2025 00:00:00 GMT http://hdl.handle.net/20.500.12323/7947 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. Tue, 18 Feb 2025 00:00:00 GMT http://hdl.handle.net/20.500.12323/7938 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. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/20.500.12323/7885 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. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/20.500.12323/7765 2024-01-01T00:00:00Z