Browsing by Author "Guseinov, GS"

Now showing 1 - 15 of 15

Citation - WoS: 47
Citation - Scopus: 55
Basics of Riemann Delta and Nabla Integration on Time Scales
(Taylor & Francis Ltd, 2002) Guseinov, GS; Kaymakçalan, B; Mathematics
In this paper we introduce and investigate the concepts of Riemann's delta and nabla integrals on time scales. Main theorems of the integral calculus on time scales are proved.
Citation - WoS: 6
Citation - Scopus: 6
A Boundary Value Problem for Second Order Nonlinear Difference Equations on the Semi-Infinite Interval
(Taylor & Francis Ltd, 2002) Guseinov, GS; Mathematics
In this paper, we consider a boundary value problem (BVP) for nonlinear difference equations on the discrete semi-axis in which the left-hand side being a second order linear difference expression belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l(2) and is formed via boundary conditions at a starting point and at infinity. Existence and uniqueness results for solutions of the considered BVP are established.
A boundary value problem for second-order nonlinear difference equations on the integers
(Cambridge Univ Press, 2005) Dal, F; Guseinov, GS; Mathematics
In this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z, under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l(2) and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.
Citation - WoS: 28
Citation - Scopus: 28
Boundary Value Problems for Second Order Nonlinear Differential Equations on Infinite Intervals
(Academic Press inc Elsevier Science, 2004) Guseinov, GS; Yaslan, I; Mathematics
In this paper, we consider boundary value problems for nonlinear differential equations on the semi-axis (0, infinity) and also on the whole axis (-infinity, infinity), under the assumption that the left-hand side being a second order linear differential expression belongs to the Weyl limit-circle case. The boundary value problems are considered in the Hilbert spaces L-2(0, infinity) and L-2(-infinity, infinity), and include boundary conditions at infinity. The existence and uniqueness results for solutions of the considered boundary value problems are established. (C) 2003 Elsevier Inc. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 8
Completeness of the Eigenvectors of a Dissipative Second Order Difference Operator: Dedicated To Lynn Erbe on the Occasion of His 65th Birthday
(Taylor & Francis Ltd, 2002) Guseinov, GS; Mathematics
In this paper we consider a dissipative linear operator generated in the Hilbert space l(2) by a second order difference expression on the semi-axis (in other words, by an infinite Jacobi matrix) in the Weyl-Hamburger limit-circle case. This operator is constructed via a boundary condition at infinity. We prove the completeness in 2 of the system of eigenvectors and associated vectors of the dissipative operator which is considered.
Citation - WoS: 6
Discrete calculus of variations
(Amer inst Physics, 2004) Guseinov, GS; Mathematics
The continuous calculus of variations is concerned mainly with the determination of minima or maxima of certain definite integrals involving unknown functions. In this paper, a discrete calculus of variations for sums is treated, including the discrete Euler-Lagrange equation.
Citation - WoS: 63
Improper Integrals on Time Scales
(Dynamic Publishers, inc, 2003) Bohner, M; Guseinov, GS; Mathematics
In this paper we study improper integrals on time scales. We also give some mean value theorems for integrals on time scales, which are used in the proof of an analogue of the classical Dirichlet-Abel test for improper integrals.
Citation - WoS: 3
Instability Intervals of a Hill's Equation With Piecewise Constant and Alternating Coefficient
(Pergamon-elsevier Science Ltd, 2004) Guseinov, GS; Karaca, IY; Mathematics
In this paper, we obtain asymptotic formulas for eigenvalues of the periodic and the semiperiodic boundary value problems associated with a Hill's equation having piecewise constant and alternating coefficient. As a corollary, it is shown that the lengths of instability intervals of the considered Hill's equation tend to infinity. (C) 2004 Elsevier Ltd. All rights reserved.
Citation - WoS: 40
Citation - Scopus: 44
Integrable Equations on Time Scales -: Art. No. 113510
(Amer inst Physics, 2005) Gürses, M; Guseinov, GS; Silindir, B; Mathematics
Integrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on K-q). We formulate the Gel'fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over q-numbers (q-difference equations). We formulate the GD formalism also in terms of shift operators for all regular-discrete time scales. We give a method allowing to construct the recursion operators for integrable systems on time scales. Finally, we give a trace formula on time scales and then construct infinitely many conserved quantities (Casimirs) of the integrable systems on time scales. (c) 2005 American Institute of Physics.
Citation - WoS: 271
Citation - Scopus: 299
Integration on Time Scales
(Academic Press inc Elsevier Science, 2003) Guseinov, GS; Hüseyin, Hüseyin Şirin; Hüseyin, Hüseyin Şirin; Mathematics; Mathematics
In this paper we study the process of Riemann and Lebesgue integration oil time scales. The relationship of the Riemann and Lebesgue integrals is considered and a criterion for Riemann integrability is established. (C) 2003 Elsevier Inc. All rights reserved.
Citation - WoS: 78
Citation - Scopus: 85
Lyapunov inequalities for discrete linear Hamiltonian systems
(Pergamon-elsevier Science Ltd, 2003) Guseinov, GS; Kaymakçalan, B; Mathematics
In this paper, we present some Lyapunov type inequalities for discrete linear scalar Hamiltonian systems when the coefficient c(t) is not necessarily nonnegative valued and when the end-points are not necessarily usual zeros, but rather, generalized zeros. Applying these inequalities, we obtain some disconjugacy and stability criteria for discrete Hamiltonian systems. (C) 2003 Elsevier Science Ltd. All rights reserved.
Citation - WoS: 84
Citation - Scopus: 94
Multiple Integration on Time Scales
(Dynamic Publishers, inc, 2005) Bohner, M; Guseinov, GS; Mathematics; Mathematics
In this paper an introduction to integration theory for multivariable functions on time scales is given. Such an integral calculus can be used to develop a theory of partial dynamic equations on time scales in order to unify and extend the usual partial differential equations and partial difference equations.
On the Riemann Integration on Time Scales
(Crc Press-taylor & Francis Group, 2004) Guseinov, GS; Kaymakçalan, B; Mathematics
In this paper we introduce and investigate the concepts of Riemann's delta and nabla integrals on time scales. Main theorems of the integral calculus on time scales are proved.
Citation - WoS: 80
Citation - Scopus: 91
Partial Differentiation on Time Scales
(Dynamic Publishers, inc, 2004) Bohner, M; Guseinov, GS; Mathematics; Mathematics
In this paper a differential calculus for multivariable functions on time scales is presented. Such a calculus can be used to develop a theory of partial dynamic equations on time scales in order to unify and extend the usual partial differential and partial difference equations.
Citation - WoS: 3
Citation - Scopus: 3
Properties of Discrete Composition Operators
(Taylor & Francis Ltd, 2005) Dal, F; Guseinov, GS; Mathematics
In this paper, we study the continuity and boundedness properties of the composition operator Fy ( t )= f ( t , y ( t )), where t is a discrete independent variable. A necessary and sufficient condition for the acting of F from a space p 1 ( p 1 greater than or equal to1) into another p 2 ( p 2 greater than or equal to1) is also established.