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Article Citation - WoS: 33Citation - Scopus: 46Higher-Order Self-Adjoint Boundary-Value Problems on Time Scales(Elsevier Science Bv, 2006) Anderson, Douglas R.; Guseinov, Gusein Sh.; Hoffacker, JoanIn this study, higher-order self-adjoint differential expressions on time scales and their associated self-adjoint boundary conditions are discussed. The symmetry property of the corresponding Green's functions is shown, together with specific formulas of Green's functions for select time scales. (c) 2005 Elsevier B.V. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 16The Laplace Transform on Isolated Time Scales(Pergamon-elsevier Science Ltd, 2010) Bohner, Martin; Guseinov, Gusein Sh.Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classical theorem of Titchmarsh for the usual continuous convolution. (C) 2010 Elsevier Ltd. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1An Inverse Problem for Two Spectra of Complex Finite Jacobi Matrices(Tech Science Press, 2012) Guseinov, Gusein Sh.; MathematicsThis paper deals with the inverse spectral problem for two spectra of finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit algorithm of reconstruction of the matrix from the two spectra is given.Article Citation - WoS: 10Citation - Scopus: 12On an Inverse Problem for Two Spectra of Finite Jacobi Matrices(Elsevier Science inc, 2012) Guseinov, Gusein Sh.We solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 7On the Impulsive Boundary Value Problems for Nonlinear Hamiltonian Systems(Wiley, 2016) Guseinov, Gusein Sh.In this work, we deal with two-point boundary value problems for nonlinear impulsive Hamiltonian systems with sub-linear or linear growth. A theorem based on the Schauder fixed point theorem is established, which gives a result that yields existence of solutions without implications that solutions must be unique. An upper bound for the solution is also established. Examples are given to illustrate the main result. Copyright (C) 2016 John Wiley & Sons, Ltd.Article Citation - WoS: 55Citation - Scopus: 68The h-laplace and q-laplace Transforms(Academic Press inc Elsevier Science, 2010) Bohner, Martin; Guseinov, Gusein Sh.Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail. (c) 2009 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3An Inverse Spectral Problem for Complex Jacobi Matrices(Elsevier, 2010) Guseinov, Gusein Sh.We introduce the concept of generalized spectral function for finite order complex Jacobi matrices and solve the inverse problem with respect to the generalized spectral function. The results obtained can be used for solving of initial-boundary value problems for finite nonlinear Toda lattices with the complex-valued initial conditions by means of the inverse spectral problem method. (C) 2009 Elsevier B.V. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 7Solution of the Finite Complex Toda Lattice by the Method of Inverse Spectral Problem(Elsevier Science inc, 2013) Huseynov, Aydin; Guseinov, Gusein Sh.We show that the finite Toda lattice with complex-valued initial data can be integrated by the method of inverse spectral problem. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem with respect to the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the solution of the inverse spectral problem with respect to the time-dependent spectral data we reconstruct the time-dependent Jacobi matrix and hence the desired solution of the finite complex Toda lattice. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 77Citation - Scopus: 85Double Integral Calculus of Variations on Time Scales(Pergamon-elsevier Science Ltd, 2007) Bohner, Martin; Guseinov, Gusein Sh.We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation. (C) 2007 Elsevier Ltd. All rights reserved.Article Citation - WoS: 12Citation - Scopus: 12Boundary Value Problems for Nonlinear Impulsive Hamiltonian Systems(Elsevier Science Bv, 2014) Guseinov, Gusein Sh.We study two point boundary value problems for nonlinear impulsive Hamiltonian systems. Spectral analysis of the corresponding linear impulsive Hamiltonian system and a fixed point theorem are employed to obtain an existence and uniqueness result for solutions of the nonlinear problem. Two examples are given in which the main condition is made explicit. (C) 2013 Elsevier B.V. All rights reserved.
