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Author: Guseinov, GSScopus Q: Q3

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Now showing 1 - 5 of 5
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    Article
    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
    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.
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    Article
    Citation - WoS: 52
    Citation - Scopus: 61
    Basics of Riemann Delta and Nabla Integration on Time Scales
    (Taylor & Francis Ltd, 2002) Guseinov, GS; Kaymakçalan, B
    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.
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    Article
    Citation - WoS: 44
    Citation - Scopus: 46
    Integrable Equations on Time Scales -: Art. No. 113510
    (Amer inst Physics, 2005) Gürses, M; Guseinov, GS; Silindir, B
    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.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Properties of Discrete Composition Operators
    (Taylor & Francis Ltd, 2005) Dal, F; Guseinov, GS
    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.
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    Article
    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
    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.