A finite-sum representation for solutions for the Jacobi operator

Details A finite-sum representation for solutions for the Jacobi operator A finite-sum representation for solutions for the Jacobi operator

2009-07-03

arxiv.org/abs/0907.0664v1

Journal of Difference Equations and Applications, 2011, v. 17, No. 4, 567--575

Physics

Mathematical Physics

To be published in Journal of Difference Equations and Applications

Scientific paper

10.1080/10236190903158990

We obtain a finite-sum representation for the general solution of the Jacobi second-order difference equation D(p(n-1)Du(n-1))+q(n)u(n)=l r(n)u(n) in terms of a nonvanishing solution corresponding to some fixed value of the spectral parameter l=l_0. Applications of this representation to some results on the boundedness of solutions are given as well as illustrating examples.

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