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Article Citation - WoS: 6Citation - Scopus: 6A Boundary Value Problem for Second Order Nonlinear Difference Equations on the Semi-Infinite Interval(Taylor & Francis Ltd, 2002) Guseinov, GSIn 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.Article Citation - WoS: 8Citation - Scopus: 8Completeness 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, GSIn 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.
