Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.Comment: 23 page

Positive periodic solutions for nonlinear difference equations with periodic coefficients

WOS: 000079460000010We prove the existence of positive solutions of second-order nonlinear difference equations on a finite discrete segment with periodic boundary conditions. Obtained results yield positive periodic solutions of the equation on the whole discrete axis, provided that the coefficients are periodic. (C) 1999 Academic Press

On a disconjugacy criterion for second order dynamic equations on time scales

WOS: 000175021700015In this paper a sufficient condition for disconjugacy of second order Delta-differential equations on time scales is given. For this purpose a mean value result on time scales is employed. (C) 2002 Elsevier Science B,V. All rights reserved